This answer may fall somewhat into sophistry...
The term "Beta Reader" comes from Software Development, where you have "beta testers". This, in turn, comes from the terminology used by IBM to describe their release life cycle:
- Pre-Alpha : Work in progress, before first full build.
- Alpha : First viable product build. This may not contain all final features, and may contain features which will be cut.
- Beta : First feature complete build. While (in theory) the software is fully usable, it may contain significant bugs / issues to fix
- Silver (a.k.a. "Release Candidate") : Known issues have been fixed or mitigated and, unless new major issues are discovered, can be released without embarrassing the creators. This is often considered to be a special type of Beta.
- Gold (a.k.a. "Production Release") : The final Release Candidate, which has passed all testing and verification. This is a 'promoted' Silver, and is what goes out to customers.
Strictly speaking, a "Beta Reader" should then not be before the second full-draft. You can also have "Alpha Readers" (who examine the story from the perspective of a reader before it is complete, to identify where things will need to be added or removed) and, most commonly in Professional Publishing, "Critique Partners" (other writers who examine the story from the perspective of an author) and "Proofreaders" (who examine only the spelling and grammar, but to not comment on the content)
Many people will refer to Alpha Readers (and sometime Critique Partners or Proofreaders) as Beta Readers, but it is often useful to (for reasons that Mary mentions in comments) keep your Alpha Readers and Beta Readers separate. This way, you can get a fresh perspective from someone who isn't remembering, anticipating, or looking for old plot points / plot holes that have since been removed, and won't be thrown off stride as much by new ones you have introduced. (Think of all the people complaining "but they changed this and that" when a book is adapted for TV or Cinema, versus the people who never read the book!)
As such - and, this is my subjective opinion, so feel free to disagree:
- Alpha Readers: Once the first draft is finished. These are to help you find gaping plot holes that need fixing, or boring / irrelevant parts of the story that changing or removing.
- Beta Readers: Once the Alpha Readers can no longer find large flaws or holes in your plot, and you no longer need to add / remove subplots, story arcs or characters. Try to make these different people from the Alpha Readers.
- Critique Partners: As early as you think you won't be too embarrassed. Because they are looking at your work as another author, they will probably be more sensitive to things like trope-usage or writing style than an average reader. You can try joining a writers circle / writing club to get this advice, and to help provide it to others. They can sometimes help to shape and direct the plot, before the first draft is complete.
- Proofreaders: Frequently. Very frequently. Definitely after every draft, but possibly within drafts too - you can get software to do a cursory examination between chapters, but they often miss edge-cases or obscure / unusual situations. Ideally, the Alpha and Beta readers don't get to see anything until it has been proofread.
Note that "Critique Partners" and "Proofreaders" are often available as trained professionals for hire. Alpha and Beta Readers typically are not, because you're looking for the reactions of a normal reader or fan.