I think the problem I have with this statement is that you're talking about the Democratic Party when you're talking about the left and you're talking about the "Heart of Conservatism" when talking about conservatism. The issue with that is that you are creating a false equivalency. As a Progressive/Socialist, I do not like Biden and do not support Biden's moderate policies. So claiming that Biden is not a successful President is not the gotcha you think it is.
For example, do Conservatives think we should move to a society free of money where all of your needs are provided to by some nebulous state and where all lifestyles are giving tacit acceptance. Either the Heart of Conservatism has greatly changed or I guess I'm a Conservative.
And like others have pointed out, the GOP is not pro-LGBT as much as they realize it's a losing battle. That is not an endorsement and should not be treated as such.