Nobody likes voting for the “lesser of two evils.” Casting a vote in favor of someone who is diametrically opposed to your viewpoint(s) absolutely sucks. The shitty reality is that we aren’t going to change the electoral process in the next two months.
If you don’t see either major candidate as a champion that you can support, it seems more beneficial to see it as selecting your enemy for the next four years. I would rather fight against someone that I have a chance of changing. At minimum I would rather protest against someone that I think has a lower chance of authorizing lethal force against a march that I attend.
Voting for a 3rd presidential candidate (or not voting at all), is letting someone else make that decision for you.
That said, we have got to get out of this constant cycle of only having two options. There’s too much money at a national level to start there. We’ve got to start local and get third party candidates into offices at a city level, then state, then national. It’s going to take a long time and it should have happened so very long ago. We can’t change the past, we can only change the future. The only time to start changing the future is in the present.
You don't protest so the president feels bad and changes things. This will not happen, they are not your friends who happen to be ignorant.
You protest so the people wake up and demand change.
The Israeli genocide and campus protests have shown that liberals will happily ignore or even side with the Democratic party no matter what, even on the issue of supporting genocide, while police storm the encampments and arrest/beat people who oppose said genocide.
Trump is better for protests id anything, because more people are willing to protest Trump (think how massive the BLM protests were) than are willing to protest the Dems, and neither party are interested in just giving you what you want anyway.