Edit: I'm not making comments about Trump's actions (specifically, I'm not defending what he did). As for whether this particular list stands up to scrutiny, that question should have been asked a long time ago.
What happened was Obama signed the bill imposing exceptions to the Visa Waiver Program in December 2015, and then his own DHS added the current list of middle eastern nations in February 2016.
It is the most tenuous argument to act like that was the work of the GOP.
Bannon is a genius. The fact that he can co-opt partisans in the deflection of criticism with facile ideas like "Obama did it" is terrifying.
That was taken directly from a bill Hillary Clinton co-sponsored years earlier (though obviously with far less context or nuance).
They're very mindful to use some sort of liberal precedent when fanning their flames, giving them (and their flock) plenty of retaliatory talking points.
One reason this is interesting is that there there were some very widely-circulated - and of course false - claims on social media that the choice of countries was somehow influenced by Trump's business interests, and that the fact no-one from countries on the list had killed in the US proved Trump was inspired by racism or even an outright fascist. https://twitter.com/JamesMelville/status/825473088758374400 was typical of the genre. Snopes decided to show an uncharacteristic lack of interest in online rumours by not mentioning them. Naturally, the same people who were spreading those claims are now spreading the debunkings about how no, Trump's ban is nothing like Obama's.