I say it is, because it is a powerful but wholly unaccountable institution which tries to impose its dogmatic rules on everyone. It’s authoritarian, and it’s officially all-male. The source of its power and authority is its imaginary relationship to an imaginary god.
Those features taken together are enough on their own to make it an intrinsically immoral institution. It bosses people, on the basis of an invisible unaccountable god, and it answers to no one. That’s a god-based dictatorship, and that’s intrinsically immoral. It excludes half of humanity from even the possibility of sharing its power, and that’s intrinsically immoral.
And those features aren’t all. There’s its long long history of murderous persecution of “heretics” and other rebels against its arbitrary unaccountable power. There’s the squalid history of the Vatican as a state. There’s the blood-chilling history of Ireland’s industrial “schools” and Magdalen laundries. There’s Savita Halappanavar. And there is of course the sprawling history of child-rape by priests and the church’s refusal to obey the law and report its child-raping employees to the police.
What’s on the other side of the ledger? Well there’s charity work. Yes, there’s charity work, but it comes with strings attached – it’s Catholic charity work. It’s anti-abortion charity work, which can be way too high a price to pay. It’s charity work that can cloak child-raping priests. It’s charity work that gives the church a toehold in desperately poor countries, so that it can spread its power even more. Above all it’s charity work that doesn’t need to be theistic in nature, and shouldn’t depend on compliance with theistic rules to be available. It’s charity work in exchange for obedience, and that’s not a good exchange.
On the other hand there are generous, liberal Catholics who do the charity without making it depend on compliance. But then it’s just charity; it’s independent of the “Catholic” part; it’s often in outright defiance of the Catholic part. (Hence the Vatican’s bullying of the US nuns.)
If the church were a golf club that formally excluded women, I would say that was immoral but not necessarily intrinsically immoral. But the Catholic church has more power over people than does a golf club. Much more. It has enormous power, and it has no truck with democracy or equality or accountability at all. Yes, that’s intrinsically immoral.