It isn't quite contradictory but it does skirt the line for a few reasons. The big one being is that conservatism seeks to, well, conserve the status quo, hence the name.
As a non-heterosexual (or non-majority individual in general) one's best interests lie with disrupting the current state of affairs.
Add to that the fact that the right wing has historically worked ardently against LGBTQ issues (and keeps working against them: either seeking curtailment or removal of equal rights)... well it makes it ideologically tricky.
Now on the economic side of things: it is far less contradictory, at least in theory. Because of the historical marginalization of LGBTQ individuals, we are (statistically speaking) more likely to be less well off than our peers (note that (in the USA at least) sexuality is not a universally protected class and thus a reason to be fired).
Lastly these effects are magnified if the individual is Trans, Non-Binary, Gender queer, or essentially "non cis-gendered homosexual". To go for conservatism has a feel or "I got mine so what do I care" in regards to Rights and Equality... which is made worse since a lot of the frontliners for "Gay" rights have been other members of the letter rainbow.
But at the same time: beliving that a free market is ideal and helpful to society is a valid worldview... as long as one doesn't ignore that groups that benefited (for free) from others' work ought pay for that labor... and that majorities can be assholes so perhaps it'd be best not to trust them all that entirely with one's rights.
So tldr: no it isn't necessarily contradictory, but it can come off as a bit self-centered and possibly working against one's self interest.
I hope this helps.
