I would submit this is not polite vs. impolite. However, it is possible your formality and politeness in language is construed, possibly misconstrued, as personal conservativism, which can then be extrapolated by the reader to political conservativism. In other words, to the online stranger, because you are not quickly or overly familiar you have conservative values. I think "polite" or "impolite" is a misnomer here.
This is part of what attracted me to Mr. Rath. In his case, he is personally conservative. He is NOT politically conservative, and neither am I. But, for instance, I am careful with my money, I like tidiness, we live simply, our children are well behaved.
I would not generalize polite or impolite to politics. I might be on firmer ground generalizing familiar behavior - and it is possible to make an argument that a politically liberal person might behave more familiarly in a quick fashion. After all - politics are values and at it's core liberalism is about progressiveness. But at the same time, I've known conservative gals that were familiar, open, and warm also.
Ultimately, politics in the US are much more complicated than they seem from the outside.