There are an ever-increasing number of opinions you can be fired for. Those doing the firing don’t use the word “heresy” to describe them, but structurally they’re equivalent. Structurally there are two distinctive things about heresy: (1) that it takes priority over the question of truth or falsity, and (2) that it outweighs everything else the speaker has done.
For example, when someone calls a statement “x-ist,” they’re also implicitly saying that this is the end of the discussion. They do not, having said this, go on to consider whether the statement is true or not. Using such labels is the conversational equivalent of signalling an exception. That’s one of the reasons they’re used: to end a discussion.
If you find yourself talking to someone who uses these labels a lot, it might be worthwhile to ask them explicitly if they believe any babies are being thrown out with the bathwater. Can a statement be x-ist, for whatever value of x, and also true? If the answer is yes, then they’re admitting to banning the truth. That’s obvious enough that I’d guess most would answer no. But if they answer no, it’s easy to show that they’re mistaken, and that in practice such labels are applied to statements regardless of their truth or falsity.