If the current Pope, or perhaps a future Pope, were to permit [active] homosexuals to receive Communion, could a [heterosexual] Catholic legitimately justify his/her remaining an active member of the Catholic Church, since it would seem that such Papal permission would be an act that teaches contrary to the deposit of faith?
I will preface my answer by saying that the situation is unlikely, because, as the original poster says, such a disciplinary decision would imply a tacit recognition on the Church’s part that homosexual actions can be legitimate. (Homosexual tendencies are never at issue, only acting on those tendencies.) That is a matter that touches on the Church’s clear doctrine that such acts cannot be approved. (It is not, however, exactly the same as a magisterial teaching of doctrine—see below.)
Moreover, as a pastoral measure, such a course of action would not (in the Church’s view) be very merciful, because it would tend to prolong situations (e.g., homosexual relationships) that in fact are very damaging for the persons involved. Not only that, but (as St. Paul teaches in 1 Cor. 11:29: “For anyone who eats and drinks [the Body and Blood of Christ] without discerning the body eats and drinks judgment on himself”) receiving the Eucharist while at the same time engaging in actions that are clearly immoral is not beneficial.
Nevertheless, in the hypothetical scenario that a Pope were to authorize Communion for persons habitually acting on their homosexual tendencies, there would still be no reason for the rest of the faithful to leave the Catholic Church. Such a change would undoubtedly be an error, from a pastoral point of view (for the reasons explained above), but it is not precisely an error in teaching.
According to the Church’s teaching, the Church in general (and the Pope, when acting in the name of the Church—i.e., ex cathedra) is infallible when it proclaims doctrine (whether that be in matters of faith or in matters of morality). However, it only teaches infallibly when it intends to do so: when the pastors of the Church (the bishops in communion with the Bishop of Rome, or, sometimes, the Bishop of Rome acting in the name of the whole Church) declare something as part of the deposit of faith. This is done in different ways, the most solemn of which are the dogmatic definitions of ecumenical councils (and on occasion of the Pope himself).
However, in a change in discipline of this kind—however flawed and not recommendable it may be—the Pope does not have the intention to teach doctrine, much less do so infallibly.
The faithful have a duty to pray for their pastors—the Pope included—and even to let him know, respectfully, if one of their disciplinary decisions is not a good idea. However, such a situation would not be the occasion for leaving the Church; rather, for seeking to reform it (always in charity, and in accordance with the Gospel) from within.
You should not receive communion in a state of mortal sin. And thats true even if a priest or pope allows it. The reason being that if you receive communion in s state of sin, you are putting yourself at a great risk as Paul puts it in 1 Corinthians 11
27So then, whoever eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of sinning against the body and blood of the Lord. 28Everyone ought to examine themselves before they eat of the bread and drink from the cup. 29For those who eat and drink without discerning the body of Christ eat and drink judgment on themselves. 30That is why many among you are weak and sick, and a number of you have fallen asleep.
I guess the point you are trying to make is IF the pope changes a teaching concerning faith or morals, will you continue to be a member of the Catholic church? And here is my take on it:
I believe that the Catholic church is the true church that Jesus founded because in Matthew 16:18-19, Jesus tells Peter
"And I tell you that you are Peter,b and on this rock I will build my church, and the gates of Hades will not overcome it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will bed bound in heaven, and whatever you loose on earth will bee loosed in heaven."
And later on Jesus in Luke 22:31-32 says
“Simon, Simon, Satan has asked to sift all of you as wheat. But I have prayed for you, Simon, that your faith may not fail. And when you have turned back, strengthen your brothers.”
The way the Catholic church has always interpreted these verses is that the Holy Spirit protects the church and the teachings that were given by Jesus to his disciples. So logically speaking if the church changes its teaching on faith and morals and teaches that sinful ways are ok, then the gates of hell have prevailed against the church and Jesus's promise to protect HIS church has failed. So if you trust what Jesus said that he founded a church, it is important to realize that he promised to protect it and if that promise fails, then Christianity fails logically.