They _may_ have no weight, indeed, as your anecdote illustrates.
People tend to empathize more with people they have something in common with (some research suggests [0][1]), so I think many of us would certainly have a mindset affected by our minority-held sexual orientation, in matters where our sexual orientation actually plays a role (security being one of the more obvious cases).
[0]: http://psp.sagepub.com/content/36/3/398 [1]: http://journals.cambridge.org/action/displayAbstract?fromPag...