As painful a read as that was, I think it's really important to understand what the social norms were at that time. Thousands of people had died and the reaction, not just from the press secretary but from the press pool at large, was to laugh and joke. Really the only widely socially acceptable response to even the mere thought of gay male sexuality was complete and utter disgust. If you were a man, to not express disgust at this thought opened the door to "you might be a fairy too", which is why you see so many of these displays of "the banality of evil".

Audio from those press conferences is available at https://www.youtube.com/watch?v=yAzDn7tE1lU

There was also Reagan's surgeon general, C. Everett Koop, who seems to have taken HIV/AIDS seriously and opposed stigmatization:

https://www.hiv.gov/blog/in-memoriam-c-everett-koop/