That is called Transubstantiation and it is a daily recurring miracle. Miracles, by definition, are God bending the rules of physics, which He created and continually sustains, and is thus allowed to bend. This is philosophical but logically consistent.
> Or believing in a literal virgin birth?
Another miracle.
> insisting on priest celibacy
That's a rule, and put there for a very good reason. The less divided your heart is by worldly cares, the more you can care only for the people God put in your care.
> keeping women out of the priesthood
Just as much as men are kept out of giving birth. Consider this quote from G. K. Chesterton: "How can it be a large career to tell other people's children about the Rule of Three, and a small career to tell one's own children about the universe? How can it be broad to be the same thing to everyone, and narrow to be everything to someone? No. A woman's function is laborious, but because it is gigantic, not because it is minute."
> are just as capable of claiming the good parts of Christian philosophy, without insisting on the parts which clearly just exist due to the the Roman Catholic penchant for power wrangling and hierarchies.
They say "you are saved by faith alone" and "the Bible is the sole authority on religion" and yet the Bible literally says "you are not saved by faith alone". That's plenty enough to disregard all their remaining arguments in my opinion.
After using the process of elimination, only the Catholic Church's doctrines remain intact.
And #3 and #4 are directly at odds. You say Priests are not allowed to have children, which is why they are celibate (fair enough) but we all know children can't be born without both a Father and Mother involved. So when men choose not to have children for the priesthood, it's seen as noble. But Women aren't given that same choice in your view (Except they are, because nuns exist, yet Nuns cannot ever actually lead the Church).
Why don't you admit that the reason the Catholic church does not allow women priests is not because "a women's function is laborious" (a function not all women naturally can even do, otherwise why can't barren women be priests?), but rather because you take the words of Paul literally and do not allow a woman to hold authority over a man? That's the real reason and you know it.
Also, the "faith alone" thing is a bit misunderstood to be honest, mostly caused by how protestants overload that word. They basically mean that you cannot be saved by works alone under any circumstance, and that if you are unable to produce any works but have faith, you can still be saved (the example here is the penitent thief on the cross). After that, they consider works to be a natural outcome of legitimate faith, and that if you have the chance to do works and don't you'll lose your justification by faith.
There's a sermon by Wesley on that here: http://wesley.nnu.edu/john-wesley/the-sermons-of-john-wesley...
It is not intellectually dishonest to believe that God, who governs the universe and it's laws is able to suspend them if he so chooses.
> Why don't you admit that the reason the Catholic church does not allow women priests is not because "a women's function is laborious" (a function not all women naturally can even do, otherwise why can't barren women be priests?), but rather because you take the words of Paul literally and do not allow a woman to hold authority over a man? That's the real reason and you know it.
No, that is not the real reason. The idea that men and women are complementary is rooted in Christian teaching since the beginning. My understanding is that the reason women are not allowed to be priests is partly because during mass the priest stands in for Christ ( in persona Christi ) and Christ was born a man. Women hold authority over men all the time in the Catholic church, many doctors of the Church are women.
> Also, the "faith alone" thing is a bit misunderstood to be honest, mostly caused by how protestants overload that word. They basically mean that you cannot be saved by works alone under any circumstance, and that if you are unable to produce any works but have faith, you can still be saved (the example here is the penitent thief on the cross). After that, they consider works to be a natural outcome of legitimate faith, and that if you have the chance to do works and don't you'll lose your justification by faith.
This is just a long winded way of saying you are not saved by faith alone.
St. John Paul II talked a lot about this subject about 45 years ago, here's a PDF with a clickable table of contents: https://d2wldr9tsuuj1b.cloudfront.net/2232/documents/2016/9/...
Roman Catholicism says that communion will turn wine and bread into literal flesh and blood. How on earth is that "compatible with intellectual integrity"? Or believing in a literal virgin birth? Another thing I can't intellectually justify is insisting on priest celibacy and keeping women out of the priesthood.
I'm not going to debate in favor of Islam, but it seems that mainstream protestant beliefs (or at least those which I'm familiar with, the beliefs of United Methodism) are just as capable of claiming the good parts of Christian philosophy, without insisting on the parts which clearly just exist due to the the Roman Catholic penchant for power wrangling and hierarchies.