I'm new to this area of stack overflow, so I can't comment as to whether a tag of this sort would be overused.
That being said, I can think of many specific questions that can be asked that would be specific ( "how do i tell them I'm gay / a different gender" ) where this would apply and potentially useful. And many more questions that relate to different groups within the LGBT community.
just to add ( and in relation to the other answer posted) I think we need to be careful when judging whether the tag relates to the question or not, where from a hetereonormative point of view these may only be adjacent to the question itself, yet may actually be central to the point - or at least of particular interest to those in the LGBT+ communities.
a good example of this might be a question where the OP might ask a question along the lines of "I've recently PreP, who should I tell?".
In addition i'd say that the use of the tag be questioned in a comment before being removed - eg. in a question along the lines of "I'm in a heterosexual relationship - how do I....",may seem like there is no need for the tag. The fact the OP may be bisexual (and may not have stated such) might actually effect the question, and require the question to be edited rather than the tag removed.
In regards to which choice of letter to use, I'd have suggested LGBT+ , frankly there is always someone who'll complain that there are too many/not enough letters. Surely an explanation on a wiki page stating that the letters choosen when the best attempt at a choice that was always going to be problematic