Added Sep 26 2019: I'm not going to do an analysis or summary of these responses – but I and others think it would be interesting to do so. If you'd like to do so, I'd welcome that and will link your summary/analysis in the top of this post here. All the data is accessible in the Google Spreadsheet below.
Submit your answers anonymously here: https://docs.google.com/forms/d/e/1FAIpQLSfiUmvT4Z6hXIk_1xAh9u-VcNzERUPyWGmJjJQypZb943Pjsg/viewform?usp=sf_link
See the results here: https://docs.google.com/forms/d/e/1FAIpQLSfiUmvT4Z6hXIk_1xAh9u-VcNzERUPyWGmJjJQypZb943Pjsg/viewanalytics?usp=form_confirm
And you can see all responses beyond just the first 100 here: https://docs.google.com/spreadsheets/d/1D-2QX9PiiisE2_yQZeQuX4QskH57VnuAEF4c3YlPJIA/edit?usp=sharing
Inspired by: http://www.paulgraham.com/say.html
Let's start with a test: Do you have any opinions that you would be reluctant to express in front of a group of your peers?
If the answer is no, you might want to stop and think about that. If everything you believe is something you're supposed to believe, could that possibly be a coincidence? Odds are it isn't. Odds are you just think what you're told.
Why this is a valuable exercise
Some would ask, why would one want to do this? Why deliberately go poking around among nasty, disreputable ideas? Why look under rocks?
I do it, first of all, for the same reason I did look under rocks as a kid: plain curiosity. And I'm especially curious about anything that's forbidden. Let me see and decide for myself.
Second, I do it because I don't like the idea of being mistaken. If, like other eras, we believe things that will later seem ridiculous, I want to know what they are so that I, at least, can avoid believing them.
Third, I do it because it's good for the brain. To do good work you need a brain that can go anywhere. And you especially need a brain that's in the habit of going where it's not supposed to.
Great work tends to grow out of ideas that others have overlooked, and no idea is so overlooked as one that's unthinkable. Natural selection, for example. It's so simple. Why didn't anyone think of it before? Well, that is all too obvious. Darwin himself was careful to tiptoe around the implications of his theory. He wanted to spend his time thinking about biology, not arguing with people who accused him of being an atheist.
Thanks to Khorton for the suggestion to do it as a Google form.
I might have more to say later. On (1), I want to state that, to me, my position seems like the conservative one. If certain views are being politically silenced, my sense is that it's good for people to have the opportunity to state that. In the alternative, people are only allowed to do this if you already believe that they're subject to unfair political pressure. Looking over the list and thinking "Hm, about 100 people say they feel silenced or that their opinions feel taboo, but I think they're wrong about being silenced (or else I think that their opinions should be taboo!), so they shouldn't have this outlet to say that" seems like a strong case for a potential correlated failure. Like, I don't fully trust my own personal sense of which of the listed positions actually is and isn't taboo in this way, and would feel quite bad dictating who was allowed to anonymously say they felt politically pressured based on who I believed was being politically pressured.