I've probably harbored more disdain for Kyrie Irving than anyone on the planet. And it definitely detracted from my life. I'd respect his position, however, if I felt it was genuine (e.g., he spoke with professionals (doctors, scientists, etc) and made an informed decision to take an unpopular stance).
Seems doubtful, though. I guess it's possible he's anti-vax, but very few people are truly anti-vax, even including those for religious beliefs. May be more likely that he sees vax mandates as a social justice issue; that fits with the data of vax hesitancy, and he is an activist (e.g., even bought George Floyd's mom a house). Maybe those are true motivating factors. But I can't shake the notion that he enjoys drama, needs to be the center of attention (maybe more so in BKN next to Harden and KD), is injury-prone (and may not mind resting for half a season), and has some other ulterior motive(s).
Regardless, I hope teammates/players defend his decision. It is his body, and if we're judging his decision based on personal beliefs (interpretations of science, morality, religion, etc), then context is also important. Pro athletes and big corporations have defended some pretty outrageous in the past, and there are countless pro athletes who have committed violent crimes and enjoying the salary and fame associated with playing on our TVs every night.