I don't know the future, so this is speculative, but it's hard to see at this stage how the Roman church can pull out of the death spiral facing other mainline denominations. Because it's so big, it may take a long time to die, like the Ottoman empire.
Consider an illustration. From what I've read, shipbuilders try to make large vessels resistant to sinking by subdividing the hull into a series of watertight bulkheads. If the hull is punctured in one place, the entire hull doesn't fill with water. Instead, you have compartments sealed off from other compartments.
If, however, several bulkheads are punctured, then the ship may keel over. The question is whether enough bulkheads have been punctured for the Roman church capsize. Given the extent of the damage, can it right itself?
Take a comparison: back in the 60s, the SBC was trending liberal. However, I believe this was centered in some SBC educational institutions (Baptist colleges and seminaries). The laity was generally conservative, and many pastors, including megachurch pastors, were conservative. It was therefore possible to change course. The fundamentals were sound. But we don't have that situation in the Roman church.
i) After initial opposition, the Roman Church has made peace with theistic evolution. Some of the most strident critics of intelligent design theory are Roman Catholics.
Although there are individuals who can espouse theistic evolution while retaining other elements of traditional orthodoxy, I don't know of any denomination that's maintained that balance.
ii) After initial opposition, the Roman church capitulated to German higher criticism. To my knowledge, this is pervasive. From top to bottom. Popes. The Roman episcopate. The priesthood. Catholic colleges and seminaries. Theologians and Bible scholars. The exception is pop Catholic apologists who converted from Evangelicalism.
A fundamental principle of Christian theology is that Scripture is a historical record of divine words and actions rather than a collection of parables to illustrate doctrine. Once you deny the historicity of Scripture and the prophetic foresight of Scripture, you lose the foundation for theology. At that point there's no reason to believe in a God who intervenes in human history. Who speaks and acts.
Moreover, if you think the infallibility of Scripture is incredible, how can you think the infallibility of the church is credible?
iii) In the Roman episcopate, some bishops are known to be liberal. Yet despite their liberal reputation, they are promoted to key positions of leadership in the Roman Church, viz. archbishoprics, congregations in the Roman Curia. These are very influential policy positions.
What does it say about a denomination where this is both tolerated and facilitated? And how does that impact theology and praxis over time?
iv) According to an estimate from 15 years ago (by Fr. Donald Cozzens), the American priesthood might be 60% homosexual, with a higher percentage among younger priests. That means the priesthood is becoming increasingly homosexual. It is worse now than 15 years ago. Although that has specific reference to the American scene, the situation seems comparable in the EU and UK.
In that respect, the moral and theological degeneration of the Roman church is far more advanced than any other mainline denomination.
v) This is aggravated by the acute priest shortage. What would happen if the Vatican were to defrock all its homosexual priests? There wouldn't be enough manpower to keep it going.
This gives homosexuals within the Roman church enormous leverage. Imagine the impact if they were to stage a walkout? The Roman church has become utterly dependent on homosexuals to keep the machinery running. Given their disproportionate bargaining power, they can dictate terms and conditions.
vi) The Vatican takes the presence of homosexual priests for granted. It regards that as acceptable so long as they are celibate–with a wink and a nod.
vii) And it's not just priests. In addition, it's a given that you have homosexual bishops. Their identity may not be widely known to the laity, but it's an open secret to their colleagues and assistants.
Even by Catholic standards, no denomination can retain traditional orthodoxy when you have that liberalizing counteraction. That's bound to move Catholic theology and praxis increasingly to the left. Which, not coincidentally, is exactly what we're seeing underway.