You call it out. You tell the people who say those things that they are not worthy of the term 'civilised'. What you don't do (and this isn't aimed at you) is to slide around the matter, hide your head in the sand and say you've not actually seen any threats (so I've had to post some - from the very link in the op) and even claim that those receiving the threats brought it on themselves and...get this...might have actually intended to be threatened.
What you can also do is to check to see what you are posting isn't the twisted thoughts of some homophobic low life who has an internet connection and a hatred of gay people. What you could do, rather than passing on these type of atrocious claims to any number of people is to check them out. Especially as it should be blatantly obvious that to claim that the leader of the choir group, a well respected local figure who is also a well respected and well known lawyer, could hold either position as a convicted child rapist.
Well, I guess we can wait until a gay person has been killed and then do something. Now, where could I possibly find an example of a gay person being killed simply because he or she was gay...gee, it may take me some time. Perhaps you could find an example. Or maybe dozens.