...The right wing billionaires play the full political spectrum: they fund causes they believe it, they fund the Republican Party and they fund conservative and libertarian institutions to push their ideology, which they fully and completely embrace. The centrist and liberal millionaires and billionaires not so much. They narrowly choose their issue, whether it's education or something else and refuse to fund ongoing ideologically based institutions. At this point, that's tantamount to working for the other side.The problem is that most billionaires are primarily concerned with making (and keeping) lots of money. That's actually true of most millionaires as well. People that are not super focused on making lots of money don't generally make lots of money.
One of our political parties is primarily concerned with making sure millionaires and billionaires get to keep as much money as possible. The other is (nominally) concerned with universal equality (of opportunity). So if you are a right-wing billionaire, then you are pretty much 100% behind the GOP: both you pet issues and your personal ones are served by them. If you are a left-wing billionaire, on the other hand, it is most likely only your pet issues are (nominally) served by Democrats.
Things changed through the 90's and 00's as Democrats changed to be more friendly to Wall Street (to the expense of the country), but still, even our right-of-center Democratic president occasionally talks about the rich/banker types as being a part of the problem, and having responsibility to pay their fair share (even though he really doesn't do anything about that).