Though a lot of voters like or dislike a candidate on the basis of emotion, there is a core of people who normally think about issues and values.
Here are some differences between the two camps on how to achieve specific ends.
1. Defending the nation. CSs like Trump suggest torture, which is against the Eighth Amendment, and killing the families of terrorists especially going after their wives, which is against the prohibition of bills of attainder in Article I, Section 9, Clause 3,
CCs are outraged at the prospect of disobeying any major Constitutional provision especially those that have to do with human rights. So, CCs are adamantly against using torture to defend the country or bill of attainder tactics that target relatives of traitors.
2. Wanting jobs to remain in America. To keep jobs in America, Trump threatens Carrier, a company that is moving production facilities to Mexico, with punitive taxes.
CCs want American jobs to remain in America and thus propose cutting business taxes to entice businesses to stay but not punishing businesses from leaving the U.S. CCs are against a Berlin Wall tax that keeps people from freely leaving the country (whether companies or individuals).
3. Media fairness. Trump thinks the way to make that happen is to strengthen libel laws so that negative articles against politicians are subject to lawsuit and financial and punitive damages. Of course, that would apply not only big media, but bloggers who publish online. CCs also want the media to be fair but reject the idea that politicians need more shelter from public, media or opposing candidate criticism. CCs want a strong First Amendment.
Is there a way to bridge the gap? There seemed to be when Sarah Palin was carrying the Common Sense conservative banner. She didn't suggest unconstitutional means to get to her ends. But, now that Trump is its poster boy, aside from accepting a trashing of the Constitution and its values, there doesn't seem to be a path to get Constitutional conservatives to agree to Trump's Common Sense conservative means.