Would be interesting to do a follow-up on whether politicians are aware of this (and if they are, whether they believe that having a "no nuance" party position is still electorally better than following the public)

Yes, I think politicians are keenly aware of the need to compromise, but of course they also believe they have to keep the core purist base engaged. Our result suggests that tradeoff may be less acute than they realize. Will think about it.