Think tanks have always been biased. Cato's biased libertarian. Brookings is biased moderate left. Actually, people
have always been biased. My guess is that the president of Heritage has always voted for the Republican Party. If the president of Heritage was a current Republican senator, that might be a little more problematic. DeMint is not a current representative of the Republican Party, so he has no non-ideological (i.e. monetary or electoral) incentive to be biased. I'm sure he's ideologically biased. So is every other think tank. And every other person.
Plus, sometimes, the partisans are right. If there's a yes/no issue, a Republican says yes, and a Democrat says no, one of them is right. That doesn't change in academia. Partisan hacks can sometimes tell the truth. My favorite example: James Dobson is literally paid to preach the gospel. But when he says "Jesus is the Son of God," I don't think anyone says "well obviously you believe that -- you're paid to believe that."
Debate the warrants, not the source. If the argument you read is a logical argument (especially a philosophical/moral/normative argument), then it really doesn't matter who the source is. If Heritage says "killing is bad," it doesn't matter that "OMGZ HERITAGE IS REPUBLICAN." The argument can be true, no matter who said it. If the argument you read is an empirical argument, then there's a little more problem.
But even then, you just can't say "that study is from Heritage, and Heritage is Republican, so the study is wrong. OK, let's move on." The better way to do it is to read the study, realize there's no methodology (as Isaiah points out), and say "this study is bad, and here are studies that have real methodology."
So you are saying it is impossible to be a conservative or a liberal and be unbiased
Yes. It's impossible to eliminate bias, although it is possible to suppress it.
Your definition of who is unbiased and biased is going to be, by definition, biased by your point of view. How can you measure if someone is unbiased or not? There's no such thing as being unbiased.