It is all about language. Music Theory is just a language that lets musicians communicate and like any language there is grammar. So first of all let me say you are at liberty to do whatever you want just like a person can use Shakespearean Middle English words like betwixt and anent. However if you just want to communicate and be understood without controversy, there is a grammar to follow.
It is all based on the circle of fifths. If you look at the circle, one side is typified by sharps and the other side is typified by flats. So when talking about a key like G or D or A or E, you keep all the notes sharp. Same thing on the other side of the circle.
And there is a reason. For example the key of Ab has four flat notes. If you use the enharmonic key of G# that key has 8 sharps. It is simpler to use Ab than G# and since this is a language, simplicity is always the key. You want to express yourself as simply as possible.
The thread was using A# as an example. I know of only 2 instances when A# is used. It is used as the 7th degree of the key of B. B is on the sharp side of the circle of fifths with 5 sharps ( whereas its enharmonic equivalent Cb has 7 flats). Then there's the controversial key of Gb/F#. Gb has 6 flats and F# has 6 sharps so that there is no advantage to either enharmonic key. However, if you conceive of the key as F#, the 3rd degree is A#. So in the keys of B an F# are the only time I have seen A# as opposed to Bb.
I should add that I am currently using A# because I am improvising with the E altered scale. Since E is on the sharp side of the circle of 5ths, I use the notes E F G G# A# C D. That A# could be a Bb except when working in E you always use sharps.
That should be enough to get things started. Obviously I just touched on some aspects of this topic. Let's see where people want to take it.