Leftists won the last three big wars, so even most of today's "conservatives" are more than a little hybridized. You won't find any independent clade of wolves who bark for their own separate wolf reasons. Barking is a marker of dogness, egalitarianism is a marker of leftness.
What about people who support school choice, believe government should be local, and are strongly pro-life, but who believe in equality of potential and thus the need for equality of opportunity among all people? Lots of those people exist.
I think you're making the very common mistake of thinking about transmitted traditions phenotypically, rather than genetically/cladistically. This methodology leads you to wander around comparing birds to bats.
The question that enables rigorous analysis is always: "where did these ideas come from?" Some people invent ideas on their own, but that's so rare it's lost in the noise.
It's very, very unlikely that your hypothetical observer looked at the world and concluded independently that all members of the species Homo sapiens have equal potential.
First, this person would have to be thinking independently, which is very rare. Second, there is no empirical evidence for this proposition -- or at least, none has ever been brought to my attention. (Fortunately, equality of potential is by no means the only reason to believe in equality of opportunity.)
If I observe that someone is a Catholic, which is more likely: that he learned his Catholicism from another Catholic? Or that he independently derived the Trinity from empirical evidence?
Your hypothetical observer may have derived his or her opinions about school choice and local government from personal observation. More likely, they came from Rush Limbaugh. Their opinions on human biology are straight-up American humanism, ie, leftism. (With nontrivial historical links to Christianity, but that's a separate conversation.) So... a wolf-dog.