The definitions and action of “Democrat” and “Republican” voters are fluid. If you subscribe to the party platform of the GOP, you are - for the most part - a Republican. I would guess that very few people here at FR would subscribe to the Democratic Party platform.
The problem is that there is no overriding definition of “Conservative” or “Conservatism.” There is not an organized Conservative Party with a platform that voters can judge. I consider myself conservative when it comes to government spending and federal overreach, but I don’t concern myself much with cultural issues like gay rights because they don’t affect my day-to-day life. I’ve been running cows for more than 30 years. Whether two men or two women can get married in Indiana or Utah doesn’t affect my ranch. Federal overreach and a smorgasboard of federal regulations do.
“Conservatives” need to form their own third party with an identifiable platform or align themselves with the party whose platform they agree with most. Politics is the art of compromise. No one - conservatives, moderates, liberals or extremists - can get their way all the time or always elect the candidates they support. And since there is no organized, registered and recognized conservative party, I would hope that most conservatives align with the Republican Party and support those candidates in the general election.
If you like conservative ideas on limited government and economics, but are liberal on social issues and weak on national defense, then you should look at the Libertarian party.
One can’t have social liberalism and limited government and conservative economics, but libertarians can’t figure that out.