"However I don't see how re-posting anti-Trump tweets on your home social media would get you in trouble, its not like disliking Trump brings the civil service into disrepute."
Unless said person is visiting the US and their social media is examined along with their other details such as current employer.
There are a couple of issues that are being conflated.
1) On the internet, things are remembered for a long time. So while you have your first amendment freedoms, you may want to think before you post. Or use an alias.
2) DHS using your social media profiles to question you when you isn't a bad thing. In a prior post I talked about being able to flag a potential terrorist. There is evidence that during the screening process, social media posts were not considered. If they were... it would have been easier to spot and deny entrance to would be bad guys.
3) What would cause you to be flagged in the first place?
Saying negative anti-Trump things? Hardly unless they were actual threats. (He's the sitting POTUS so threatening him is a crime.) But saying something like "I don't like Trump because he lies and claims that his plants are bugged ..." Or something even sillier, isn't going to get you in trouble.
The whole idea is that when they swipe your biometric passport, they can pull up your social media accounts. Actually they would have pulled up the profiles prior to your boarding or even while on the flight.
Its a non issue. If they want to pull up my social media accounts, all they would find is my LinkedIn profile.
There's nothing there that would be of interest to anyone from any country.