Marvel created an Avenger team with a mutant leader specifically to call this issue out. For the past 3 years this has been a strong focus in the comics. It's an interesting subject to bring up. It's not like there have never been celebrity mutants in the comics as well, and the initial outcast then acceptance makes for a more important story and message then everyone hates mutants. There's no growth in that.
In the films The X-Men have not saved anyone really in the general public eye. So why would they hail them? None of that has even been explored much. All that's really been put out there is the government side of things and that these guys have potentially dangerous powers that they may not be able to control. Which many of them can't, even under the guidance of Prof X. Who wouldn't be afraid of that? There's mutants always causing damage. They have to actually develop more with humans and prove why the X-Men are good guys to the public in the films to move anything forward in that regard. While there will always be those who are afraid of people who are different, there is not just negativity and rejection.
Of course celebrity superheros in films like Stark, Johnny Storm and Cap get attention, they save cities and humans in front of everyone. The government doesn't like them either, heck that's gonna be an MCU story next year. With every hero comes naysayers and cheerleaders. Part of the job, look at Batman.
I agree they don't need the term mutant. It's useless without having a majority of the characters. And the only ones beside Pietro and Wanda they can use for their benefit at the moment would be Wolverine (Avengers) and Storm (Black Panther). More so Strom imo.