Just for context, Lindsey Graham asked the escort his age and the escort said he was 18. This also occurred back before real IDs that got scanned and when people 18-21 often had fake IDs for drinking. In other words, it's not like if Graham asked for Kelvin's ID that it would have proved things.
“I just need you to tell me how old you are,” Graham allegedly said at one point, according to Kelvin’s account.
“I said, ‘OK, I am 18 years old,’ ” Kelvin recalled.
It was also still constitutional to ban gay sex and gay people couldn't get married. He was also an older gay person, not particularly good looking, and still wanted to have sex, which meant paying for escorts, which was illegal already. I don't think this really shows that Lindsey Graham was some sort of evil person. He grew up with his very existence being illegal, he still couldn't legally get married, and so existing inherently meant violating laws he had been taught one way or another. He at least tried to make sure this victim was an adult.
I'm not saying Lindsey Graham wasn't horrible. He often voted against LGBT rights. But... he made something of himself as a closeted gay person during a time in which it was nearly impossible to be out. If he had come out at some point, he would have lost his career, been a public joke among conservatives, and ultimately he chose to stay in the closet.