I just googled up a transcript of the part of the interview which dealt with his labeling himself conservative...
When Sawyer asked if Jenner cheered when Obama became the first president to even say the word “transgender” in a State of the Union address, the 65-year-old replied that he “would certainly give him credit for that.”
“But not to get political,” Jenner continued, “I’ve never been a big fan, I’m kind of more on the conservative side.”
“Are you a Republican?” Sawyer asked in response, to which Jenner replied, “Yeah! Is that a bad thing? I believe in the constitution.”
“Do you think that would be an unsettling thing for some people in the conservative wing of the party?” Sawyer asked.
“I’ve thought about that,” says Jenner, adding that neither political party has a monopoly on understanding.
So the only clarification he's providing for calling himself conservative is: "I believe in the Constitution".
Actually, I'm guessing that it's just he chose the wrong term for himself. I think it likely that if he had a better understanding of political labels, he would probably prefer to label himself "libertarian" rather than "conservative". But that's just my speculation, so who knows.