Youtube and later on Twitch got into trouble with the RIAA and other major media groups because Youtube allows users to upload copyrighted material. I believe the result of the lawsuit vs Viacom was that Google has to make a reasonable attempt to keep copyright material off Youtube which brought about the ContentID system.
Circling this back to Parler, Twitter and Facebook both have the same type of "hate speech" that Parler does that would violate Google's, Apple's, and AWS ToS but the difference is they can make the claim they make a "reasonable attempt" to keep those comments off while Parler does not.
There's also the argument that now that the Democrats are in charge, the heads at FAANG is increasingly worried about regulation and getting broken up so it's in their best interest to take a harder stance on this. I think the coming months will be very interesting.