> Who appointed Ajit Pai to the FCC in the first place?
The FCC by law cannot have more than three commissioners from the same party. The sitting President therefore finds himself in the position of having to appoint up to two commissioners who are NOT from his own party.
I don't think that there is any actual requirement for how the President picks such nominees--so a Democratic President needing to appoint a non-Democrat could in theory choose someone from some left-leaning non-Democrat party like the Green party, and a Republican President could choose someone from a right-leaning non-Republican party, such as the Libertarian party.
In practice, though, what Presidents of both parties usually (always?) have done is ask other party leadership [1] for a name, and then the President nominates that person.
When the nominee comes up for confirmation in the Senate, generally the Senators from each party pretty much automatically vote to confirm the nominees from the other party unless there is something that actually disqualifies them. They don't vote no just because they disagree on ideological grounds.
So yes, Obama originally put Pai on the FCC, but you can't really read anything into that as far as Democrat positions goes. Pai was the choice of Republican leadership for one of the two seats that could not go to a Democrat.
People are too focused on Pai here. Getting rid of net neutrality is in the freaking GOP party platform. By winning the White House, Republicans won a majority on the FCC. It didn't matter which existing Republican commissioner they elevated to the chairmanship (Pai or O'Reilly) or if they made their new, third guy chair (Carr). Whoever they picked was going to do this.
[1] Usually whoever leads the other party in the Senate, I believe.