Jesus supported the Old Testament, according to the Bible Jesus saw the Old Testament as literal. So, I imagine that Jesus saw Leviticus and its contents to be valid.

Matthew 5:17-18 Common English Bible (CEB) Jesus and the Law

17 “Don’t even begin to think that I have come to do away with the Law and the Prophets. I haven’t come to do away with them but to fulfill them. 18 I say to you very seriously that as long as heaven and earth exist, neither the smallest letter nor even the smallest stroke of a pen will be erased from the Law until everything there becomes a reality.

I actually find Matthew 24:37-39 to be one of the most interesting verses in the Bible. Jesus is a young Earth creationist.

Matthew 24:37-39 Common English Bible (CEB) 37 As it was in the time of Noah, so it will be at the coming of the Human One.[a] 38 In those days before the flood, people were eating and drinking, marrying and giving in marriage, until the day Noah entered the ark. 39 They didn’t know what was happening until the flood came and swept them all away. The coming of the Human One[b] will be like that.

While Jesus said nothing about gays, I'd would imagine that he shared his father's (his own) bigoted views.