Private companies can place standards of conduct in regard to posting statements on private property.  There is no clear violation of the 1st Amendment in regard to ABC.

 The US Government however can not require it in this case.  I'm not sure that griping about what a human posts on social media is considered coercion, even if it is a US Political Official.  The whole "We have reached out to ABC, they have said they will be taking action, so we will see what they do" in itself is not incriminating as the WH can "reach out" without making demands.

 The lawsuit makes the issue more complex, so there could be grounds for a 1st Amendment violation when all variables are combined, but I'd say its not the strongest argument.  This is an opinion.