The reasons why Ronald Reagan wouldn’t fit into todays Republican Party is because he believed in both economic and personal freedom. Reagan was a real Conservative in the Libertarian sense not religious or neoconservative sense. He didn’t believe government's job was to tell people how to live their own lives, or was skeptical about personal freedom. Which would’ve been a big problem with him with Neoconservative Republicans.
Ron Reagan wouldn't fit in with today's GOP at least the Christian-Right and far-right in general because he believed in Separation of Church and State. He didn't believe the job of government was to act as the national father and that Uncle Sam and perhaps Father Sam if the Christian-Right were to come to power, was to make sure that all of his children were living a traditional and their American way of life. And not doing anything that the Christian-Right sees as immoral, even if innocent people aren't being hurt.
And yes President Reagan was tough on national security and foreign policy, but he believed in those things so America wouldn’t have to police the world. Rather than being as strong as we had to be so we could police the world. And Reagan believed in the same thing that Richard Nixon did when it came to foreign policy. Which is peace through strength, which is that you are as strong as you can be so you don’t have to use all of your power that you are so strong that other countries and terrorists would be crazy to want to attack you.
President Reagan didn't believe in nation building, or have some right-wing utopian fantasy that we could change a part of the world that still lives in the 1500s culturally and still to a certain extent legally and modernize them and force liberal democracy and individual rights on them. Reagan's national security and foreign policy was about American interests and strengths and protecting our freedom. Not forcing our way of life onto other countries that live light years behind us and still see women as servants to men.
As well as Reagan believing in that you had to work with your allies for the simple reasons that they know important things that you don’t, but also so you don’t have to police the world. A difference between an internationalist, liberal or conservative and a neoconservative, is the internationalist bases their national security and foreign policy based on realism and the facts on the ground. Sees the world for the way it is and does their best with those realities to make it the best that they can.
The neoconservative is the right-wing utopian. If they were left-wing they would be Socialists, but the right-wing utopian sees the world for the way they want it to be. And ignores reality or doesn't understand it and does everything they can to make sure what they see in their political fantasy comes to real life for the rest of us that are sober and not needing mental therapy because of our sanity. And decides the utopian was right all along and that this is the way it is. Reagan was a realist, not a utopian.