Science does get suppressed when its conclusions are considered politically incorrect or unfortunate. That's exactly why politically convienent and fortunate research is so suspicious--any dissenting research is automatically disqualified, so it has the appearance of truth when really it's just systemically one-sided.
No it doesn't. As far as I know, the opposite thing happens: politically motivated research that doesn't deserve to be called scientific gets published over and over again. I'm specifically thinking about a few "scientific" articles sponsored by oil companies that happen to explain away global climate change, for instance. Or the many papers in which the Cato foundation, earnestly and with the best of intentions no doubt, tries to establish the inferiority of public healthcare. Or the Genesis Foundation defense of creationism.
If you take a step back, one man's convenient is another man's inconvenient. And don't think for a minute that science limits itself to pissing off rightwingers. Nature has a way of pissing all over all sorts of ideological preferences. There's nothing about the laws of the universe that force, say, human biology to work in a way that suits a given political agenda. One day it might seem to be on your side, another day not so much.
Ultimately when politically sensitive research is allowed to happen, independently confirmed (or disconfirmed), and slowly digested in a mature fashion on all sides of the political spectrum (no "ha I told you so!" and systematic over-interpretation, no knee-jerk "the only explanation is political bias and the research must stop"), society surely stands to benefit from a more realistic and nuanced worldview in which to decide on policy. Not easy to achieve of course, but it makes me sad when people fail at the first hurdle.
