What could Mozilla have done with W3C making HTML5 DRM (EME) part of the official spec?

That stance is the main reason W3C lost support from the community (They not only lost Mozilla but also EFF and a lot of trust from independent developers).

That DRM affair was also conducted in a very shady way with secret votes, etc...

W3C didn't loose Mozilla over EME. 1) Mozilla is still an active participant in W3C (there are many more things than HTML there) 2) Mozilla supported EME. Maybe reluctantly, but supported it nonetheless.

Lost trust from a small but very vocal bunch of disruptive people and others who don't know what that actual issue is but seemed like a good band wagon to jump on grrrr big business giving it to the man!