So in other words their argument will be that not much has changed (except maybe now it is a single manchild vs. a bunch of children).
Free speech in the Constitutional sense (not that that applies to a private platform anyway) is primarily about freedom of political speech (as opposed to say yelling fire in a crowded theater or threats of violence). I don't think it extends to impersonating others though unless it IS obviously parody. I'm quite certain however that while it may be obvious to you and me there will literally be millions of twitter users who it will not be obvious to. They will see Elon's name and Elon's picture and assume it is from Elon. The blue checkmark next to the name even reinforces that. I doubt those individual were trying to parody Elon Musk so much as they were trying to get themselves banned to prove some kind of point. From the first twitter screenshot it looks like a warning was given about labeling something as parody when impersonating someone. It's hard to see that as some egregious violation of free speech. A warning no doubt ignored in order to become a Twitter martyr.
In any case, whether or not it is about suppressing speech of those of a certain political affiliation depends on how equally the policy is enforced. It can't really be argued that Elon is suppressing those of a certain political affiliation if he does the same for all political affiliations. Whether that's happening or not, I don't know. Remains to be seen I guess. Right now I suspect it is mostly those of a certain political persuasion doing this to prove a point so it will look a little one-sided right now regardless.