In one way, protesting doesn't achieve anything - it'll rarely change decisions or sway policy that's already in place (especially with someone as delusional as Trump).
But it shows loudly that people aren't happy, and offers some solidarity and comfort to others who are outraged.
And assuming history has some form of record which isn't suppressed or rewritten, then at least future generations will know there was some resistance.
My worry is these protests will fade in a few weeks and just be a blip - how long can people keep them up after all?
Yes ... It is VERY depressing reading comment sections or hashtags on twitter - the number of ignorant haters out there is incredible. So much for living in an enlightened, educated age.