I'd argue that in islam pretty much all of these restrictions are not applicable when it's for medical reasons. Alcohol is explicitly allowed in such cases (I think it was used to relieve pain in surgeries) , and even pork is okay to eat if you can't find anything else. Another example would be Ramadan fasting, which is not necessary if you are ill or when you are travelin.
Overall, almost any restriction in islam is very flexible when it's a matter of life or death, or if it's a medical necessity/recommendation. So, a pig valve is arguably not any different from a cow valve when it's so clearly not for regular consumption.
You can rationalize all you want, but you can't reason religious people out of things they didn't reason themselves into. If these people can be convinced that they shouldn't be doing thing XYZ on the order of an omnipotent being that nobody has ever seen, chances seem to be even between them accepting exceptions from this order and them rejecting these exceptions. After all, you see other people rejecting/ignoring other parts of their own religion all the time.
It's not rationalization, I know some religions have a pretty rigid structure that you need to rationalize your way around when it comes to medical exceptions to religious rules but... Islam is not one of them. Maybe some folk belief might be a source of hesitation in this case but in islam the jurisprudence is very clear and no scholar would really argue otherwise. Just to give an example, even ISIS allowed alcohol to be used for medical reasons if prescribed by a doctor! I'm Muslim and have a pretty good grasp of the beliefs of the different islamic branches/sects/schools and I've rarely came across an example of restrictions not being waived for medical reasons, though it's very possible I've missed some examples.
But you're still arguing about perfectly following a set of arbitrary rules. The very fact that they're arbitrary means you'll get people who'll make up arbitrary religious rules for themselves (and they will perfectly follow those) and the "beliefs of the different islamic branches/sects/schools" will be no more relevant for the beliefs of an individual than a codified national language is for some people's idiolects.
They are not arbitrary though. Historic, perhaps. E.g. pork was disallowed as far as I know due to the spread of diseases from bad conservation techniques at the time.
But that's one of the differences between faith and knowledge, namely justification. You'd be correct to claim that it's non-arbitrary if you happen to know that this justification was how it was arrived at. Randomly arriving even at a correct belief without justification would not AFAIK constitute knowledge.
IMHO this is human arrogance. It's the belief that as a human you are able to know and justify anything and everything with science and rationale, which is mostly wrong if you look at history.
I wish you were right. We got scolded for using donors’ breast milk for our newborn because donors might have eaten pork. SMH.
EDIT: I understand where you are coming from. I follow the most liberal and rational interpretation of Islam. But feel like we are very small minority.
That is very weird. Was it from the family or from an imam? I know breast milk has a few rules around it in islam, but it mostly boils down to sharing breast milk creating a form kinship between the babies sharing the milk. As in, you become in a way sister/brother with the other baby.
But I agree that many Muslims have a...lot of folk beliefs and take a lot of mental shortcuts that lead to reductive interpretations of the religion. In those cases, bringing up good Islamic jurisprudence usually works.
It was family elders. They are pretty serious about religion, attend Islamic lectures etc. And they were mostly concerned about pork consumption of donors. No one mentioned anything about forming milk kinship.
With all due respect, the worst people you can ask for religious advice would be family elder, imams in local mosques. In that order. Find someone who actually studied the religion not just someone who memorized a book.
I can't say for sure, but going from my interpretation of what seems to be the (sunni) scholarly consensus, it really shouldn't matter. Pork is not allowed to be eaten for a few reasons, none of them are relevant for cardiac valves especially considering you don't ever "consume" the pork. Pork is only allowed if you don't have another alternative when it comes to feeding yourself,but since I don't think it's restricted at all for most other uses, there's no need to even have to chose an alternative if possible. Though there is definitely a cultural repulsion towards anything related to Pork in Islamic countries so I'd definitely expect alternatives to be more popular based on that repulsion/taboo even if it's not haram
