Some of the F1 host countries have big human rights issues. But how does that affect your perception of F1?
It does not affect it in any way.
One can say politics and sports should not mix,
Yes, one can, and one should say that, exactly.
and a country's human rights aren't an issue of the series. But in these cases, politics and sports do mix. Governments use events like a Grand Prix as a way to promote the country, to hide the negative publicity those countries are getting, very much because of the same governments. And I hate how F1 is enabling that for them. I have to admit, my opinion might be different if those bad-human-rights GPs were classic races. Then it'd feel like those countries deserve to be in the calendar but now they are there just because they pay so much for a chance to promote themselves.
I have a different perspective on this. I come from a country, where the first couple of F1 events were held under a regime just like - or worse than - the current Chinese one. I was pretty happy about it, just like about everyone else who attended and watched in Hungary. You have to think about the people - the FANS - of F1 and motorsports in general too, who do not deserve the political situation and circumstances they live in, and they do deserve the opportunity of attending an F1 race at their home, at least at the time I really felt that way. I also remember at the sickening feeling the Moscow and LA olympics boycott caused.
No, trying to push politics into sport is bad, disgusting, and disruptive. Doesn't really matter who or why, which and to what end. period.