Evil doesn't exist...
I'm always reminded of a fairly recent Doctor Who episode (link):
Bill: Is everything out here evil?
The Doctor: Hardly anything is evil. But most things are hungry. Hunger looks very like evil from the wrong end of the cutlery. Or do you think that your bacon sandwich loves you back?
The core of the answer here is that good and evil are relative concepts.
Rather than "the wrong end of the cutlery", you should be focusing on "the wrong end of the plot". The plot almost inherently serves to draw that line between good and evil, or alternatively to make a point of how there is no pure good or pure evil.
"Protagonist" does not mean the same as "good". "Antagonist" does not mean the same as "evil". Pro/antagonist refer to their relation to the plot. Some examples:
- Dr Horrible's Sing Along Blog very much plays with this distinction. It's a story that follows a classic villain (protagonist), whose story arc is being hindered by a classic hero (antagonist). As we explore the characters, the villain is a sweet guy and the hero is a jerk, leading to even more juxtaposition that helps us decouple pro/antagonist from good/evil.
- The Hunchback of Notre Dame (I'm focusing on the movie because I don't remember all of the book) ends up exploring similar themes. While the protagonist is the good guy (Quasimodo) and the antagonist is the bad guy (Frollo); Frollo is shown to think of himself as the protagonist in his own story (how to liberate Paris from sin), which proves the point that what Frollo genuinely sees as good, the story's actual protagonists (Quasimodo, Esmeralda, Phoebus) consider to be evil. Contrast this to pretty much every other Disney movie, where the villain freely admits they're villainous and they pretty much revel in it.
- The Star Wars prequel trilogy follows the story of Anakin, who is already know to become Darth Vader at some point. While pre-Darth Anakin is portrayed as narrative good initially, there are telltale signs that his good/evil alignment isn't as clear cut.
...but the antagonist still looks evil...
As much as these examples decouple pro/antagonism from good/evil aligments, they still ensure that the relative evil is observed as evil by the plot.
Using the example of the Hunchback of Notre Dame (movie, not book), Frollo's justification is not fully explained. For example, had the movie contained a scene where Frollo was strongarmed by his superior (e.g. an archbishop) into doing the things he does, the plot would have painted Frollo as a pawn, rather than the source of all evil. If you then resolve the plot the same way (killing Frollo), it's not as satisfying as it was in the original version, because Frollo no longer plays the role of the source of all narrative evil.
But instead, Frollo is only shown to do his (narratively) evil deeds, and his personal justification for them. As far as the viewer can see, this behavior stems from Frollo. He's not just a cog in the machine, he is the man driving the machine.
This puts the source of the plot's evil squarely on Frollo's shoulders, and thus his death works as a meaningful plot resolution.
This doesn't mean you can't play around with this of course, but you need to understand that this leaves the plot open, as the true evil is still unresolved. This can be intentional (to start up a sequel), but you should make sure that you don't devalue your current plot resolution.
My antagonist is the leader of a group of survivors, and cares deeply for her family and group, and is extremely suspicious of my protagonist
This immediately reminds me of the Governor from the Walking Dead. He leads a peaceful colony/community, but ends up being a narrative evil villain.
When you watch the episodes, you will see that the plot, the protagonists and the viewer do not think of him as an evil character initially. Though there are some hints about his true character, he's shown to be a good leader who simply happens to conflict with Rick (the leader of the protagonists). Initially, this is painted as an understandable mistrust as either community doesn't know if they can trust the other community.
It is only when the Governor does evil deeds (torturing innocents, attacking other communities) that the story starts painting him as the narrative evil.
Nothing about what you've told me about your antagonist conclusively makes them good or evil. Caring for people does not make you good. The question is what moral line you are willing to cross in order to protect those you care about.
Victor Fries (Dr Freeze from Batman) genuinely wants to cure his wife because he deeply loves her and feels guilt for causing her "death". But he crosses the line by committing robberies and mayhem in order to get the funds for his continued research, and that (usually) paints him as the narrative antagonist despite his good intentions.
Can I still make my antagonist an effective "bad guy", despite the fact that she is, truly, lawful good?
Think about every story where the protagonist is a criminal. More often than not, the narrative evil is not necessarily evil.
Consider Commodore Norrington from Pirates of the Carribean. He fits the lawful good alignment to a tee, but he is the plot's antagonist because his actions directly oppose the destination of the protagonist's story.
Compare him to Lord Beckett, who serves as the narrative antagonist the the second and third movie. Beckett is lawful evil, not good. And while this is a very different character from Norringtion, he serves the same purpose as the antagonist.
Good/evil has nothing to do with being the antagonist, and vice versa.
...from the perspective of the protagonist's plot...
When you have one or more protagonists, then the plot is written from their point of view. They are the centerpiece of the story.
The protagonist is often genuine, at least to themselves. This means that their decisions are often based on their genuine observations. As you write the plot, you almost inevitably end up writing it in the way that the protagonist perceives the plot, because you have to use the plot to justify why the antagonist is actually an obstacle.
Going back to the Doctor Who bacon sandwich example:
- When the pig is your protagonist, the antagonist is either the butcher or the human who eats the bacon sandwich (depends on your narrative focus).
- When the human who eats the bacon sandwich is the protagonist, the antagonist is death through starvation ("the elements").
- When there is no protagonist, or the protagonist is outside of this scope (e.g. an alien observer of our planet), the pig, the human, and death through starvation are all just cogs in a machine, who are not aligned with any perception of good/evil.
Even when you don't deal with true evil, but only antagonism (e.g. most romcoms), the antagonist is often still perceived to be "the most horrible person" and is thus hated by the protagonist.
While that is likely not the objective case, the protagonist thinks it's the case. They come to that conclusion using their observations (which the plot provides) and their interpretation thereof (which their character exposition provides).
The way I constructed the antagonist's character (and according to the results of an alignment test I took from her point of view), she's lawful good. That aligns with how I see her, and how I'm writing her right now.
This is a bit of a red flag to me. You write the plot, from the plot's point of view. The plot's antagonist must appear evil to the protagonist, and therefore to the plot, and therefore to the writer's mindset when writing the plot.
Exceptions are made when your protagonist is a genuinely evil character who freely admits it (a great example here is Frank Underwood from House of Cards). When the protagonist, plot and viewer all agree that the protagonist is evil, then "good" almost inherently paints itself as the antagonist (or one of them).
When you want to describe your antagonist as good, and your protagonist thinks of themselves as good (regardless of whether they truly are good), you've run into a conflict. It's nigh impossible to objectively describe the antagonist as good, subjectively describe the protagonist as good, and then still make it clear to the viewer what point of view you're writing from.
If you do this, I suggest you let go of the notion of a signular plot with a clear protagonist and antagonist, and instead opt for a Game Of Thrones-esque "multiple players on a stage" where everyone has their own observations, intentions and experiences.
...but exceptions exist.
Tropes and literary devices are commonly used, but they can be equally valuable when subverted. I've listed some examples of stories which specifically go against the "protagonist must be the good guy" trope.
I find myself using Game of Thrones (again, I know the show better than the books) often as an example of breaking trope expectations:
- Ned Stark was bait for viewers that stick to the "plot armor protagonist" trope. Everyone identified with Ned as the "common sense" character. His removal from the story exist purely to teach viewers that just because we mostly follow one guy, does not mean that he's got plot armor.
- The Red Wedding was bait for viewers that stick to the "karma always wins" trope. Everyone considered the Starks morally justifiedi n their rebellion, and that they were owed vindication. Instead, the Red Wedding proves that good does not win by merit of it being good.
- The Red Wedding also throws Checkhov's gun right out the window. The characters who died all had personal story arcs that were nowhere near being resolved, and their deaths stopped those arcs dead in their tracks (except for Lady Stoneheart). The gun was shown to be on the mantlepiece, and then the plot decided to burn down the room and never think about it again; specifically to teach viewers that story arcs do not always tie up their loose ends.
- Most plot villains have had plenty of spotlight to showcase that they're not evil, they just respond to the way life has treated them. A basic example here is Theon's capture of Winterfell. There are only very few cases of true evil that is considered injustifiable. The only truly evil character we've seen so far is Ramsay Bolton, who is an actual psychopath. The Mountain may be another example, but it's not yet conclusively proven to be the case (we only have the Hound's point of view). The White Walkers are currently painted as evil, but we've only seen the point of view of the humans. We don't actually know if they're evil or simply have a non-nefarious purpose.
The long and short of it is that you can break tropes, but you must do so knowingly, and you have to make a clear point about intentionally breaking the trope. If you underdevelop your subverted trope, it will come across as bad writing instead of innovative plotbuilding.