Taste is not synonymous with personal preferences, otherwise we wouldn't describe some taste as "bad taste" or "poor taste." Rather, to me, one's taste refers to one's power of discernment as to what is good.
We can enjoy cup-of-noodles without conflating our enjoyment as being good taste. I like a lot of things that are fairly trash.
It doesn't need to be able to be described in objective terms to be objective, or rather to matter.
Agreed. As someone who watches an embarrassingly large number of isekai, I'm not going to drink from a public water fountain and call it a pierian spring.
Okay, but so what? "Taste is subjective" is meant to defend the existence of some thing. "Just because you don't like it doesn't mean it shouldn't exist (or shouldn't be the way it is)." Are you therefore saying the opposite? "Because most people don't like it, it shouldn't exist"?