Yes, as the basis of conservatism is protecting the heterosexual family role. Most of them still view LGBT people (especially trans today) as degenerates, perverts etc. They hate that gay marriage is legal, and you can be assured that if the death penalty was more prominent, they would want LGBT people to be sentenced.
Other than that, the LGBT community should know as much as any how it feels to be oppressed. But that is made much more difficult when you are being targeted in society by racists, as you can cover up your sexuality, but you can't change your race.
There are therefore only two reasons I can think of as to why LGBT people are conservatives: they are carrying on with adopting the same traditions that they have been raised with throughout their childhood and adolescence, and/or they have been raised in an unloving environment and have a lot of self-hate. If you were comfortable with yourself as gay/trans/bi, then you wouldn't be conservative in my view.