Well there's ALREADY a term for that. It's called a double standard. And in this case, a false one, since you've left out the fact that Trump and Obama do not have identical approaches and so there is no contradiction between being alright with one and not with the other.

It's ultimately a fabrication. The right wing taking things that the left HAVE cared about and acting like they don't. The left isn't just discovering the refugees now. They've been pushing to help them for YEARS. Obama was doing that and so got less flak than the guy who wants to shut down. The right wants to paint the left as "virtue signalling" because they don't want to acknowledge that liberals ACTUALLY give a shit. They don't just talk about wanting these things. They actually want them. They've been working towards them for YEARS. Women's rights, a path to citizenship for illegal immigrants, humanitarian aid—these are not new issues that no one talked about. They've been central parts of the Democratic platform for years.

I think you'll struggle to find ANY issue brought up by liberals these last couple weeks that wasn't.