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 do indeed generally think that whether their writings will "damage the movement" should not be particularly high in their list of considerations to think about when asking other people questions, or writing up their thoughts. I think being overly concerned with reputation has a long history of squashing intellectual generativity, and I very explicitly would not want people to feel like they have to think about how every sentence of theirs might reflect on the movement from the perspective of an uncharitable observer.
I prefer people first thinking about all the following type of considerations, and if the stakes seem high-enough, maybe also add reputation concerns, though the vast majority of time the author in question shouldn't get that far down the list (and I also note that you are advocating for a policy that is in direct conflict with at least one item on this list, which I consider to be much more important than short-term reputation concerns):
I would strongly object to the norm "before you post to the forum, think very hard about whether this will damage the reputation of the movement", which I am quite confident would ensure that very little of interest would be said on this forum, since almost all interesting ideas that have come out of EA are quite controversial to many people, and also tended to have started out in their least polished and most-repugnant form.
I also remember the closing talk of EAG 2017, with the theme being "stay weird", that explicitly advocated for being open and welcoming to people who say things that might sound strange or unpopular. I think that reflected an understanding that it is essential for EA to be very welcoming of ideas that sound off putting and heretical at first, in particular if they are otherwise likely to be punished or disincentivized by most of society.
From a blogpost by Scott Alexander:
I think a key example in this space would be a lot of the work by Brian Tomasik, whose writing I think is highly repugnant to large fractions of society, but has strongly influenced me in my thinking, and is what I consider to be one of the most valuable bodies of work to come out of the community (and to embody its core spirit, of taking ethical ideas seriously and seeing where they lead you), even though I strongly disagree with him on almost every one of his conclusions.
So no, I don't think this is a good norm, and would strongly advise against elevating that consideration to the short list of things that people actually have the mental energy for to do when posting here. Maybe when you are writing an article about EA in a major newspaper, but definitely not for this forum, the most private space for public discourse that we have, and the primary space in which we can evaluate and engage with ideas in their early stages.