What are you trying to accomplish here?
If a symbol is well known, getting that meaning out of reader's heads is very hard. Like if you decided that in your story the dollar sign, $, will be a symbol for, I don't know, a new political party, I think readers would be asking, So what does this party have to do with money? Do you mean that this party is all about economic policy? That they are corrupt and take bribes? Or what?
If your goal is simply that you need a symbol in your story for some idea or movement or group, why not just make up a new symbol? What is gained by trying to recycle an existing symbol?
The only reasons I can think of to re-using an existing symbol are:
(a) The characters in your story want to bring connotations of the existing idea into their new idea. The symbol represents something that is highly respected and they want to appropriate that respect. Like, many people see the Statue of Liberty as a symbol of freedom. So you use the Statue of Liberty as a symbol for their movement or organization so that people will associate them with freedom. (This could be legitimate, if they really are all about freedom, or it could be a total sham.)
(b) The characters are trying to tear down some existing idea, maybe are trying to replace it with their own. Like, they hate Christianity and want to replace it with their own religion, so they use a cross as their symbol and try to convince people to associate the cross with their new religion rather than the existing religion.
I'm not saying those are the only possible reasons, just the only ones that occur to me.
It may be necessary to distinguish why you as the author want to re-use a symbol, and why the characters in your story want to do this.
Either way, getting people to forget the meaning of a well-known symbol is hard. user10915156 mentioned how some programming languages use the $ to mean "variable". That's true. But I've been a programmer for 40 years (wow I'm getting old ...), and I still find that distracting. To some extent you can get people to separate "domains" in their minds, to see something as having one meaning in this domain and a different meaning in another domain. Like I recall once noticing with amusement that when I was talking about electronics, "CRT" meant "cathode ray tube", but when I was talking about war-gaming, "CRT" meant "combat results table". But I sincerely doubt that any American, even the person most wrapped up in programming forgets that "$" is a dollar symbol. I can't imagine someone going to the mall and seeing price tags and wondering why the store put variable names on all their products.