Could a Catholic justify remaining an active member of the Catholic Church if the Pope permits homosexuals to receive Communion? 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.