> Elon Musk portrays himself as an affable nerd who posts memes on Twitter
Because that's what he is.
> whereas Bezos has forgone a hair transplant and embraced the Lex Luthor look.
I'm not sure how you that makes sense. Are you saying that if Musk were bold he couldn't be an 'affable nerd'.
> In the early days of SpaceX, they filed a lawsuit asking the government to dismantle the company that was their main competitor for EELV[1] and no one blinked an eye.
Because the government was clearly engaging in totally unfair monopolistic behavior (the government having formed ULA and simply handed it all space launch contracts) that was against the rules government has for itself and SpaceX won this lawsuit.
Since then DoD launches have been handed out with a commercial competition.
SpaceX also filed a law-suit against NASA for engaging in highly anti-competitive favor granting to a competitor for the COTS program. This was recognized and since NASA has done a very good job at commercial selection.
The thing is, people (who are knowledgeable) judge you based on the details of what you do not the broad facts (X filed a lawsuit). SpaceX filed lawsuits against unfair competition and most people interested in space were aware of these unfair practices and wanted them change.
BlueOrigin in contrast profited from the progress SpaceX produced and was able to bid for all NASA programs since. There was competition, they lost, complained and lost and the sued the government (and will certainly lose again) based on what everybody understands to be terrible claims, delaying the whole government moon program.
Amazon in turn has engaged in a years long campaign trying to stop or disrupt Starlink while their own project is and was half a decade behind. Their claims are highly questionable and at times just flat nonsense and have been dismissed multiple times. However each opportunity they come back new reasons to complain. This leaves people who are observing this with only one conclusion, Amazon doesn't care about the details of Starlink proposal and their ongoing efforts with FCC, rather they are simply trying to disrupt and slow down competition.
Details and context matter.