I’ve never been given a contract that required me to post on social media. If this happens with regularity at any professional level, the actors are highly compensated for it, as they’re essentially advertising on behalf of the project.
Some contracts will require that you do not speak negatively in any public way about a production / a company or certain people involved - and while I’m sure this social media thing does happen - I haven’t heard of it. It’s probably something a publicist would handle anyway.
Here’s my feeling: always feel free to ask, but don’t expect or require free labor from actors (or anyone). Part of an actor’s job is to promote their work and the projects they’re involved in. It’s rare that isn’t to their own benefit anyway, but on low budget projects working with actors who probably don’t have a lot of time or resources to begin with, I think it’s unfair to place this additional burden on them, especially when it tends to be a ton of time and effort for very minimal if noticeable payoff.
Also, actors are in a difficult position to begin with and I think it’s unfair to further place them in position of having to be the spokesperson for a project. Our faces are on everything we do - but sometimes we take jobs we aren’t thrilled about because we’re trying to survive and build our careers to the point that we don’t have to say “yes” to every last offer we get.
I can’t think of another business where the employees are so visible and expected to represent and promote the business publicly at all times, even when they’re not working. There are certainly some parallels (I think service workers might relate), but it would be like if Intel printed Joe the Engineer’s face on every computer that had one of their microchips in it and then expected him to tweet about Intel four times a day and post selfies with their products while he was out shopping - and then to also defend Intel everytime someone on the street complained to him about a failed part.
I get that it’s part of what we sign up for as actors, but just speaking from my limited perspective as an actor, I wish more people understood how little decision-making power we have, how little influence we have unless we’re an A-list Celeb Star, and how every thing we do and say can affect our ability to get hired in the future.
Just as a relevant recent example, I think Ed Skrein did the right thing stepping down from his role in Hellboy to address the whitewashing of the character - and on the other hand, I understand some of the frustration that is being voiced in regard to how he’s being so wildly applauded for being just basically decent. But thinking about it as an actor, I know how hard that must have been to, because he risked losing his agent by doing that, maybe his manager as well, and he literally may never work again in Hollywood if he’s rubbed certain people the wrong way - and he’s definitely upset some people with the ability to block him from getting cast in the future. Hopefully, many more actors will follow his lead in doing the right thing and those people will have their hands tied.
I’ve gotten off track and this answer has gotten long, but to return to the point - if it’s valuable labor, then you should pay for it and pay well. If you can’t, then you have no business requiring it.