I don't see a reason to avoid using software hosted on GH. I moved off GH when MS bought it, and all that entailed was no longer hosting my own software on GH, and using alternative FOSS git forges. That still has a similar effect, and when a critical mass of devs move off GH, the rest will follow suit. The main draw of GH is that everything's on there; when that's no longer true, it will no longer be the main git forge. Especially once Forgejo adds ActivityPub integration; I imagine that'll speed the process along a lot.
A lone user boycotting all software hosted on GH is realistically not going to make any devs move their projects off GH. You may say that it doesn't have to be a lone user, but I think you'll be hard pressed to get a whole movement of people refusing to use any software hosted on GH.
I also think the boundaries of your boycott are just too ambiguous. What if you download the software from somewhere other than GH, and it just has a GH repo? Is that ok with you? Is it that you just don't want to touch MS's servers? What about software where the GH repo is just a read-only mirror, and the main collaboration/development happens elsewhere, like a GitLab or Forgejo instance? I would rather struggle to see an argument for refusing to use software in either of those cases.