They listen to their base. They can't afford to lose the base. It's the outreach to moderates that only happens during campaigns.
For what it's worth, they aren't actually cutting health care. There's a reason they can't get a repeal through even though they control both houses of congress and have a rubber stamp waiting in the white house.
Obamacare passed without a single Republican vote. The Republicans took over congress largely as a result of the unpopularity of the policy and the process.
Their base lost the popular vote, the MO of the modern GOP is rule by minority through any means necessary. Plus all they need to do to get their base to vote is induce moral panic about abortions or transgender people, which they're already pretty good at.
The problem for them is they have a slim margin. And there's disagreement between cutting healthcare a little bit for the moderates, or completely slashing it for the hardcore.
For what it's worth, they aren't actually cutting health care. There's a reason they can't get a repeal through even though they control both houses of congress and have a rubber stamp waiting in the white house.