Is there a more common term for that? I think it's a huge problem in polling. I googled and I didn't make much progress. I found this...
There is considerable debate about whether survey respondents regularly engage in "expressive responding" โ professing to believe something that they do not sincerely believe to show support for their in-group or hostility to an out-group.
The problem is that "expressive responding" is a technical term. At Wikipedia I searched for "expressive responding" (in double quotes) and I got zero results.
Of course that mental mindset is big deal when it comes to Trump. A recent example - Lots of Republicans suddenly think the economy wasn't that bad after all. There's not exactly a "debate" when it comes to Trump and republican voters. They always do it when Trump is involved. It's not a coincidence that the election always causes a rapid change in what they say they believe.
I think you're describing virtue signaling. The name might be misleading, but I think your description is essentially the intended purpose of such an invention