I think you are just going to have to accept they have a right to be angry and not get too caught up in the details or what they say they are angry about. Don’t get bogged down in that. Go with he general drift of the emotion and respond to that rather than in getting caught up in the thoughts and words.
Let it wash over you unless there is actual abusive behaviour or homophobia. They are very distressed in an uncomfortable and confusing situation, they are allowed to rail against the world a bit.
They are not going to be in a position to receive a discussion about the finer points of sexuality and relationships from your perspective at the moment. Perhaps never. You have no right to expect that from them and frankly it will only make things messier if you engage in that way.
Focus on the emotions not the words Receive the emotions, be there. You’re just going to have to take it and not argue back for the larger part. If it’s gets too much walk away rather than argue back. Accept that they are trying to make sense of this and just be an emotionally present bystander whilst they do that. Don’t let it turn into a deep seated hatred or anything though. Speak about your stuff to someone else not them. You need to be the supporter not the supported in this.
And also frankly, you have let them down. Embrace that and go about making it up to them in other ways as best you can. Stop grappling with the feeling of guilt, accept it and let it informs and empower your future actions. You have met them down but not irredeemably so go about redeeming yourself. No one has died.
Where guilt is useful is that it tells you were you have a feeling of responsibility or regret about something you’ve done and that points you towards putting it right as best you can and avoiding doing it again. Get on with that.
If you don’t use guilt as a spur to better action in the future then it can be a way of feeling sorry for yourself and keeping the emotional focus on you.
You do need some of your emotional focus to be on you, but you cannot expect any of their emotional focus.
Yes, you do have your own stuff to work through, and you are entitled to your feelings and to make that your focus at times. But do not do that in the context of your marriage or your relationship with children. Do it elsewhere. There are LGBT support groups for that. Or in friendships or even therapy.