Yes, I would be deeply worried if people linked to neo-nazi blogs. There is, of course, a difference between criticism of Israel and anti-semitism.
As for Hollywood, my understanding is that most people who are worried that the Jews are over-represented in Hollywood, are worried for anti-semitic reasons. Certainly, it's rare to see someone comment on it without invoking anti-semitic stereotypes or tropes in the process.
And why should anyone link to Larry Summers if not to make women feel unwelcome? He's not a famous geneticist, or a famous rationalist, or a famous expert in the world of sex-differences, or really anything else. He's mostly famous for is this speech, which is full of shoddy reasoning and anecdotal evidence.
I sympathize with your reaction. But one can go overboard with this: if the heuristics disqualifying potential sources for a view are too aggressive, then no one will be qualified to present that view, even if it turns out to be right. For instance, the disqualifying description of Summers in the above comment is questionable:
Larry Summers...He's not a famous... expert in...really anything else. He's mostly famous for is this speech,
Take a look at his wikipedia article.
He won the John Bates Clark medal, awarded to the best economists under 40, basicall...
Summary: Current social psychology research is probably on average compromised by political bias leftward. Conservative researchers are likely discriminated against in at least this field. More importantly papers and research that does not fit a liberal perspective faces greater barriers and burdens.
An article in the online publication inside higher ed on a survey on anti-conservative bias among social psychologists.
The link above is worth following. The problems that arise remind me of the situation with academic and our own ethics in light of this paper.
I can't help but think that self-assessments are probably too generous. For predictive power of how an individual behaves when the behaviour in question is undesirable, I'm more likely to take their estimate of how "colleagues" behave than their estimate of how they personally do.
This shouldn't be surprising to hear since to quote CharlieSheen: "we even have LW posters who have in academia personally experienced discrimination and harassment because of their right wing politics."
While I can see Lammers' point that this as disturbing from a fairness perspective to people grinding their way through academia and should serve as warning for right wing LessWrong readers working through the system, I find the issue of how this our heavy reliance on academia for our map of reality might lead to us inheriting such distortions of the map of reality much more concerning. Overall in light of this if a widely accepted conclusion from social psychology favours a "right wing" perspective it is more likely to be correct than if no such biases against such perspectives existed. Conclusions that favour "left wing" perspective are also somewhat less likely to be true than if no such biases existed. We should update accordingly.
I also think there are reasons to think we may have similar problems on this site.