No, they don't. That you even think that they do shows how little you about conservatives. Unfortunately the lack of knowledge about conservatives seems to quite common here on the Reader Rant.
Ah, yes... what is a Conservative these days? Thank you for putting some definition on your particular stripe, but it is one of a great many that I have seen. In fact, it is quite popular for the Regressive Conservatives to declare that Republicans are not true Conservatives - and they believe that King Kon is a True Conservative, to boot.
So you see, some of us may have a lot more knowledge of the range
of Conservatives than you do, since your definition appears to be fairly specific and exclusive. This is a glitch in the functionality of discussions, if a word carries more than one meaning.
Trying to discuss socialism (small 's') is fraught with many of the same pitfalls and traps... we can't really discuss a thing without agreeing on definitions first.