Frankly, the "beef" is fairly involved, but it comes down to the fact that we reject the concept that the Church Christ intended is the hierarchy and structures of the RCC. We disagree with many of its traditions, such as Mary being Immaculate (i.e. without original sin), the veneration of specific saints, pergatory, works-based salvation, etc. and don't believe that an institution that holds to them has any right to call itself the one, true Church. We don't think that Jesus made Peter the pope, or that there has been an unbroken apostolic succession as the RCC teaches it. We have concerns that Catholic orthodoxy can get in the way of the pure Gospel.
What bugs me in particular is the Protestant-bashing that those who are first to cry, "Catholic basher!" engage in around here. Kind of the way liberals are so quick to insist that black people need their hand up and can't fend for themselves and yet attack everyone else as being racist.
Having said that: Do we really need to be having this kind of debate and sniping today? I mean, really, does Gibson's masterpiece in any way emphasize any of the theological disagreements between us, even in the artistic elaborations? So what if he drew inspiration from a Nun's writing! If he were Protestant, he would've probably drawn inspiration from an extra-Biblical novel!
Oi vey, people.