The problem that often comes into play, here, is when people of certain political persuasions try to weaponize somebody's "feelings" against them to dismiss that person's argument:
It's lazy and manipulative at the same time.
This doesn't mean that everyone who invokes "feelings" fails to care about actual feelings. Rather, it's the suggestion that the feelings of some demographics (usually marginalized groups) are assumed to be inherently more "important" than those of people who belong to so-called majorities.