What difference does it make what they "self-identify" as? Frankly, most people are clueless. Just as one example:

People (even self-identified conservatives) favored not excluding pre-existing conditions for healthcare.
They favored free wellness, including colonoscopies.
They favored most of the elements of the ACA (I could spend time listing them if I must).

But those same self-identified conservatives didn't favor the ACA.

It isn't what they self-identify as, it's what they actually are that matters. And even that is a bit relative. By European standards, there are almost no liberals in the USA. Bernie Sanders would likely be considered a moderate in France. I've always considered myself a moderate. But depending on whom you ask, I could be labeled conservative (my grad school roommate would say that), or a "libtard" (Dope and LM and BHM would likely label me that).