Tesla wants and relies on the data collected by their proprietary system. CarPlay's privacy features would not share every button press, navigation route, music listened to, etc. while in CarPlay mode. Thus, no CarPlay for Tesla. It's really that simple. They can't build FSD without that data. I think all the rumors of butt hurt feelings over this or that by CEOs and whatnot is a smoke screen.
Rivian took a chance their offerings were unique and appealing enough to not need CarPlay, at least in the short term. I think that has played out well for them so far, but we'll see how the appeal goes long term. Doesn't hurt one of their big competitors, Cybertruck, still doesn't exist. And Cybertruck won't have CarPlay, either. So it's really Ford they have to contend with at the moment. Which, to be sure, is tough competition.
So that lack of CarPlay might start hurting Rivian in a few years time. But that's plenty of time for them to adopt CarPlay if they wish.
Lucid, playing in the luxury space, had no real option but to support CarPlay. All of their direct competitors have it.