Depends on what kind of extremism you’re talking about. Since Trump is no small government advocate, and small government advocates are numerous enough that they should have a party representing them, they would certainly have to have a big voice in any new party. And some of them would be rather extremist on that front, but that’s okay, there are extremists in the Democratic Party too who want single payer health care and free stuff for everyone.
The kind of extremism we’d be rejecting is the nativism and know-nothingism. We would do things like acknowledge that climate change is real, but not necessarily endorse big government solutions. We’d be pro-science in general, inclusive and welcoming to all. But on all the legitimate differences in ideology that people have, that are based on an INTELLECTUAL foundation rather than an emotional one, all viewpoints would be welcome. In practice, we’d be a moderate conservative party, since liberals already have the Democrats and the hardcore religious conservatives would stick with the Republicans, but we wouldn’t exclude anyone except those who preached divisiveness.