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.