If you are registered as a Republican or vote in GOP primaries in states with no partisan registration (i.e., play your part in shaping party policy and constituting the GOP electorate), then you're a real Republican. Period. Donald Trump is a Republican, and Gary Johnson is not, just as our buddy King is a Republican and the "DINOs" everyone hates from WV are not. It is normal (and a sign that you are a thinking human being) to disagree with your party platform on multiple issues.
With that said, I'd much rather the future GOP look like Gary Johnson than Donald Trump.
If you vote for one party 90%+ of the time in general elections, you are a de facto member of that party. I don't care whether you're a faux "independent" or a relic from the other party. The voting record is what tells the story.