First, this is a glimpse into his character:
Then there is the fact that Republicans hate him. Why? Because he likes science. See this entire hateful cover story done against him by the
National Review. Here is the opening paragraph:
"My great fear," Neil deGrasse Tyson told MSNBC's Chris Hayes in early June, "is that we've in fact been visited by intelligent aliens but they chose not to make contact, on the conclusion that there's no sign of intelligent life on Earth." In response to this rather standard little saw, Hayes laughed as if he had been trying marijuana for the first time.
It goes down hill from there.
The most positive thing I've heard Tyson say about Republicans, and this was a backhanded remark, was that we could get them to fund science so long as we convinced them it was good for the economy. In his words, "there is a truth--that no Republican wants to die poor."
In addition to that on virtually every social issue I've heard him speak on, he's come out as a liberal. He's even done interviews for PETA.
Not to mention that he identifies as an "agnostic" (though he's really an atheist). He's done entire presentations on the dangers of religion and how it is essentially incompatible with science.
His big thing, though, is that he doesn't want to be claimed by a particular group. He doesn't want to be known by any thing other than a scientist. So, he's always careful not to really come down too hard one way or another (see the PETA interview for example). Or, if he does, he tries to avoid totally trashing the other side.
I am unsure where he stands on economic issues like unionization and trade agreement and other such things, but I can safely say that having watched numerous interviews and the like--Tyson is a strong social liberal. That would make sense based on his background as well.