Will Rome Act on Martin, SJ?

"Fr." James Martin SJ is no longer dancing on the line.  He crossed it.

...Martin attempts to show how an explicit defense of homosexual behavior can be reconciled with Christianity in his “guide,” citing biblical scholars who allegedly help interpret Biblical passages on homosexuality. However, the advice of Martin as well as the scholars boils down to this: Even Christians can ignore Scriptural prohibitions on homosexual behavior.

Martin laments that such biblical verses “are used against LGBTQ people over and over,” and goes on to advise that “one response” to these verses “is to see them in their historical context and remember that even devout Christians shouldn’t do everything that [the] Old Testament commands. Likewise for the Epistles in the New Testament.”

His selective rejection of New Testament Scripture passages is at odds with the Catechism of the Catholic Church (CCC), according to which the authors of Scripture are inspired by the Holy Ghost, and thus, “we must acknowledge that the books of Scripture firmly, faithfully, and without error teach that truth which God, for the sake of our salvation, wished to see confided to the Sacred Scriptures.”...

Martin deliberately conflates 'ceremonial law' with 'moral law' to manufacture support for his heresy.

How long can Francis I and the homosexual network in Rome ignore this and maintain credibility as Catholic teachers/rulers?

Not long.

But if "Fr Z" is correct, no correction is forthcoming in the near term.