This is my personal experience: over the course of my life, I have held both conservative positions and more progressive ones (depending on the topic, and in different periods of my life). I have always been much more willing to discuss openly those positions that I would describe as progressive.
This is despite the fact that over the years I have been living in more than a handful of different countries, each one with different cultural norms. So I think there must be some sort of general tendency, where conservative opinions tend to be disclosed less frequently. I don't know why that is the case, and I would like to hear if anyone has an answer.
I’m similar. It’s a good question. I think it’s because there’s a pervasive underlying presupposition that conservatives are less intelligent or at least less educated than liberals, so maybe you subconsciously want to be associated with the smart, scientific group and disassociated from the uneducated, anti science group? I suspect that’s part of it in my case. Also, in my personal experience, if you want to avoid negative consequences, you’re better off keeping conservative opinions to yourself. The same is not true of progressive opinions.
Thomas Sowell's "Conflict of Visions" theory might provide better explanations. In effect, people with more left/liberal views tend to emphasise the importance of speech, ideas, things that seem expert or scientific. People with more conservative views in contrast emphasise practical experience over ideas, common sense / simple explanations over complex / expert explanations, and tend to consider speech not particularly powerful at changing minds or spreading ideas.
The above explanation is not judgemental. There are times when complex, expert arguments are correct. There are also times when people obfuscate hidden agendas behind clever sounding language. How powerful speech is at spreading ideas is a purely intuitive judgement, it's not easy to measure.
If you believe that expressing your opinion isn't particularly impactful on the world, that people who use complicated statistical methods aren't automatically trustworthy and might be obfuscating things with maths, that academic/intellectual types who talk a lot aren't really valuable to society, then automatically you'd find participating in a poll unappealing.
In contrast, if you believe speech/expressing opinions is an extremely powerful way to change the world, that experts who use maths are inherently worth supporting, that academics/intellectuals are amongst the best of us, then talking to a pollster might seem like a pretty important and virtuous way to spend your time.
The above explanation is invariant to cancel culture, sneering attitudes towards conservatives etc.
I think it also depends on the audience and group you're with. If you're moving around a lot, you might end up in expat/international/diverse groups. Most people who move to several countries aren't moving to villages 4 hours from a city and speaking and blending in with the locals and really hearing what rural people think.
Growing up in a small town and moving between small towns across the US every year or so, I never had exposure to "liberals" until I started using the internet as a teen. Until then, everyone I was ever around talked about them like they were bogeymen.
In the country I live in now, I was initially exposed to much more "progressive" opinions from people. Now I'm seen as less "that foreign guy" and more of a local, and I hear what people would normally discuss with their friends and family. It's quite different.
It's true that context counts, I can see your point since, similar to your experience, I also come from a rural area and I lived in a tiny town for some years.
But I also feel like I have a "default setting" for situations where I don't really know who I'm talking to, and in those situations, what I said above still applies.
Cancel culture is often in the back of my mind because I work in tech, however what I said above was not only referring to the workplace, so the question still stands.
Also, you are not really giving an answer, because if the cause was "cancel culture" then the next question would be why cancel culture works that way and not the other way around.
This is despite the fact that over the years I have been living in more than a handful of different countries, each one with different cultural norms. So I think there must be some sort of general tendency, where conservative opinions tend to be disclosed less frequently. I don't know why that is the case, and I would like to hear if anyone has an answer.