I think you're operating under the confused notions that (a) Catholicism is whatever the Pope decrees it to be, or that (b) a Pope's bad example is somehow binding on Catholics.
Neither proposition is true. For example, (not that there was truly any doubt) JP2 taught infallibly in Evangelium Vitae that abortion was always a grave moral evil.
There is no wiggle room in what he said, no room for compromise, and no doubt. No future Pope can cross that off the list, any more than he can decree that red is blue or that rain falls up.
As far as a Pope's bad example, the earliest known example (we'll give Peter a pass with his threefold denial because it was before Pentecost) is in Galatians 2. It was, well, a bad example, and St. Paul correctly recognized it as such.
If the Church has survived (barely, but survived) a Pope like Alexander VI, who openly kept a mistress in the Vatican and gave preferments to his illegitimate children, it can survive bishops who are wimps versus Islam. That is not to say that what they do is okay, just that it is not any kind of fatal blow like you seem to think it is.
You aren't going to like the following.
As far as the Anglicans, Lutherans, and others: Protestants went off the rails definitively in the area of sexual morality in 1930, when the Anglican Lambeth Conference decreed that artificial contraception was acceptable for married couples. That was contrary to 2000 years of established Christian teaching. Lord Runcie, the former Anglican Archbishop of Canterbury, has admitted that a church which accepts artificial contraception has no consistent, logical grounds for opposing homosexual activity. Once you endorse contraception, you endorse the idea that pleasure alone is sufficient justification for sexual acts. The conclusion that there are no grounds to restrict that pleasure solely to the married, or solely to heterosexuals, follows naturally.
What is the only major Christian denomination which sticks to the position of the Protestant reformers on artificial birth control? Hint: it's not Protestant.
But it isn't the Pope who decides what's moral. That's what wars have been fought over and Christians have died at the stake for.