A fairly simple argument for this position is: This speech (the content posted to social media) is either speech by the poster or speech by the social media company; you can't have it both ways. If the social media company isn't responsible for illegal content, then ipso facto it must be the user's speech. But then the company doesn't have first amendment rights attached to that speech itself, such as the right against compelled speech that would be implicated by this law. (Note that this law doesn't by any plausible interpretation
limit anyone's speech acts.)
I think everyone intuitively understands you can't assert 4A rights on contraband held by the police while also denying owning that contraband to dodge criminal responsibility. This thing with social media is the same thing but with 1A instead of 4A.
I would consider myself a first amendment absolutist; and yet I don't have a 1A problem with the concept of this law [0] insofar as social media companies choose the position that user speech isn't their speech. The problem is that they won't come out and state that position, they intentionally flipflop on whose speech their websites host exactly depending on what is most convenient. So of course it looks like this is a massively overreaching law when the position flops to "company speech". And if a company came out and said okay we accept responsibility for what's posted on our platform, then I'd be the first in line to say that the government can't force them to publish certain content.
Contrast traditional publishers who definitely have first amendment rights to publish or not to publish things. Well, yes, they do, but they also have legal responsibility for what they publish. The rights follow the responsibility.
[0] Saying nothing of the wording; because I'm sure it was drafted by censorious assholes, like every other law.