You can see a lot of my thoughts on Richard and his passing in the tribute section Phil gave the link to earlier but suffice to say out of all the immense talents that make up the Muppet performers, i think he would have been my alltime favorite. I understand the curiosity behind the questions of what led to his far-too-early death but also have to agree with those that say it is a very personal matter (especially given that in most ways that HIV is contracted), and if this is info that those close to him feel don't need to be included in biographical info then so be it.
It's horrible that even at the beginning of the 90's, AIDS still has such a stigma associated with it (sadly though much has changed, as a society there's still far too much unenlightened attitudes/knowledge our there) and no doubt this made his death more tragic because whatever the behind-the-scenes circumstances, there was probably more of a need to keep it his HIV status a secret...not that anyone probably thought anyone needed to know - the internet was just really starting as a means of communication and certainly no one within Henson was probably aware of how much a fan base they had at that time so why make any annoucements when "no one" would even know who Richard Hunt was? Of course that made it all the more a shock to his fans when they learned of his passing after the fact...many of us didn't even know until they saw Muppet Christmas Carol and saw Richard's name there with Jim's in the opening dedication. The only place i EVER heard anything about his death was in the obituary section of The Advocate...the very first issue i actually bought as opposed to skimming through it in the newstand...the liberation of reading it on the bus home only to have that replaced with pure shock and sadness to see an obituary for Richard (and about a month after the fact since at that time there was a bit of a turnaround time for the latest issue to hit the newstand - so there was also anger that this was the ONLY place i learned of his death - a MONTH after it happened. Maybe he wasn't the household name Jim was but it just felt like a total slight!)
Anyway, this probably seems like a lot of rambling but the point i am getting to here is that even though it was only 10 years ago, the world was very different then - if this happened today, his fans would probably have known about his HIV status and been able to send him letters of support and good wishes before he passed away - none of us got a chance to say "goodbye" or "thank you". He would have known much more how much people really loved and appreciated him. I would have given anything to have been able to express my love and gratitute whether it be a hand to hold or a hug in person or via a card...and since back then we didn't have that kind of opportunity, i think that's why some people feel more of a need to know "WHY" it all happened.
So if you still need some kind of answer to your question, i can offer the following attempt..."Why did Richard die/How did he contract AIDS? Because he was unfortunate enough to live in a time when politics and a large portion of society preferred to remain in a state of ignorance of things they'd rather ignore than put a lot of focus on saving millions of lives of all sorts of wonderful people - both in terms of being able to stem infections and putting priority on finding a cure for those who did have it." I'm sure that's not quite the answer you're looking for, but all things considered it just may be the best one that can be given.