They actually don't. You can just ignore them. I get that people find them unpleasant. But "finding somebody unpleasant" is different from "someone costs you money."
This is before the fun part where, depending on the level of "personality" you're dealing with, you might end up getting a fun weirdo who becomes obsessed with you for a little while and makes life miserable for everyone involved. I know one person who was stalked on GitHub (before they let you ban people from interacting with you, a fairly recent feature) and this person would comment on literally EVERYTHING they did, but only in a "nice" and "helpful" tone. You can't tune that shit out so easily, I'm afraid.
To be fair you also get some lesser psychopaths'; the angry guy who reported his bugs, replied and demanded to be replied to via Lisp programs in quoted code blocks was a more memorable one.
What this is saying that if your "free software project" includes anything more than providing the source code for free online--in other words, if it includes things like a bug tracker, a discussion forum, etc., that you are actually paying attention to--then it's not just a "free software project" any more, it's more like a "free website", and has many of the same issues people are discussing here relative to the latter. And the solution would be much the same: your time and effort isn't free, so if you're giving it to the project, the project shouldn't be free; you should charge for it.
If you can't automate this step, you have to read the insults, and pleading, and jerk-faced comments from the demanding users. Which takes time and energy.
Go one step further and make it a product. OP'll be a millionaire in no time.
SAAS with free tier does it this way:
* To contact support via non-app method you need a PIN. PIN is displayed when you login into your paid account. Don't have a PIN? Can't connect to support.
* To contact support via app method your profile needs to be associated with a paid account. Don't have a paid account? Can't contact support via inapp
And, look, that's not perfect and I'm not saying that it's not unpleasant. I'm saying that it's materially different from every person who uses your service costing you actual dollars. And if you can't see that, I honestly don't know what to tell you.