you need a coalition to win. if the conservative base is going to exclude certain candidates, and risk putting someone up there that won't get independent votes - they will lose.
it cuts both ways, but that's what it means to have a coalition.
Of course, the nature of any political party is exclusion. For example, no member of a group called "Communists in America" would ever be included in the pool of potential applicants for the Presidency.
So the question is not whether or not the pool of candidates will be limited to exclude candidates of incompatable ideologies: of course it will be, per the example above.
That leaves the real question, very simply, as:
A) What ideological/political positions must a Republican nominee for President have, and B) which ideological/political positions traditionally associated with the Republican party are to be considered non-mandatory?
I would like to hear your short lists for both A) and B) above.