This is a great question, surprisingly enough. I'm a fiscal and social conservative (not one is greater than the other for me) who's registered as a Republican, but I could switch to being an independent because the Republican party, the GOP, whatever you want to call them, have really hacked me off over the years. 3 reasons why I haven't switched: some people who are actually conservative I will support, I'm kind of lazy to make the switch, and I would want to make sure that whoever I support actually has the money behind him/her (independent parties, typically, don't have the money to get their name out their so 99% of the time they lose). So there's that on me. Now that I provided some context for where I'm going on this, let's answer the question.
In the modern era, if someone sees themselves as Republicans, they instantly associate themselves with Ronald Reagan because Reagan WAS a real conservative. He actually popularized the ideology, which is simply following the US Constitution and common sense. In other words, getting the government out of the way and letting people making up their own minds. At least, that's how I see it (in a brief summary). However, we had, and still have, many Republicans might have liked SOME of the things Reagan (and other conservatives today), very successful and loved, they wanted (and still want) a piece of the pie without having to work for it. For the most part, they went against what Reagan did and what he stood for. You have/had figures like Bill Krystle, John McCain, George Will, John Boehner, Karl Rove, the Bush Family (George Sr, George Jr, and Jeb), John Kasich, and many others like them, that have said good things about conservatism. However, when it came time act, they did nothing. Why, after all the things they said that would put the country on track? Simple: they were only able to round up voters, subscribers, or what have you, to make them legitimate and powerful.
When Trump, a Republican and conservative (instinctively), came and actually DID do the things that these same people suggested, the ALL came down on him and denounced his actions, even though many of these ideas, if not all of them, were theirs'. So the next question is do/did they really believe in what they were saying? The answer is no. Again, they'll say things that sound good for conservatism, but in reality, they only serve the Republican party within D.C. When another REAL conservative comes along and does and says things that are a part of the ideology, same thing happens: they get ripped apart. The point is these so called conservatives that are a part of the "Conservative Movement" are nothing more than actors trying to make themselves out to be smarter and better than everyone else. They're no different than what you see coming out of the Left, other than how they approach others.
Anymore, when someone that says they're conservative in the Republican party, I take them with a ton of salt, until they actually do something that represents conservatism properly. Ted Cruz is a true conservative. Rush Limbaugh, same deal. You also have Jim Jordan, Dan Crinshaw, Charlie Kirk, Steven Crowder, and Mark Levin. These people and many more actually practice and believe in conservatism, both fiscally and socially. These people do not follow the "Conservative Movement." Just because someone who's a Republican says they're conservative, it doesn't make it true. You can be an independent and be conservative. At the rarest of moments, they can even be Democrats that are conservative. For the most part, with regards to Republican insiders, conservatism doesn't define them, but rather their arrogance and self righteousness. These people align more-so with the Left than they do with conservatives. To be honest, I don't know why conservatives make up the base of the Republican party, other than they have the funding and there are real conservatives within positions of power. Other than those reason, the party insiders are trying to push them out or convert them to be more "moderate" (drones). This was a good one to answer because this is important to ask. Know who you're backing before you actually back them.
