It's not just making fun of a religion. It's outright saying that religion is something that causes crazed fundamentalists to perform sick acts of child abuse, probably directly caused by the passage from the bible where Abraham is asked to murder his son, Isaac.
And if you interpret it not just to be her mental delusion, it's implying that the Christian God, because it does refer directly to Christianity, exists and would actually ask a mother to brutally murder her own child.
Like, it didn't have to explain the mother's actions with a religious undertone.
That's not the same as Final Fantasy chucking in the name of a Greek god as a boss, or something having demons (which has been a part of practically all religions, so it's just a generic monster), or the gore from zombies. It directly calls the credibility of Christianity into question.
Not that I care; I'm an atheist, and I agree with the game's message, but I can see how Nintendo would want to stay away from that. If I were head of Ninty I wouldn't go near Binding of Isaac with a 50 foot barge pole.
tl;dr Religion is a touchy subject for people, especially when you're insulting fundamentalists, and it's not in Nintendo's best interest to publish a game whose underlying story is a massive stab at one religious group.
Edit: And also @Zantigo, what are you on about "Do you really think a large corporation ran by fucking Japanese people give a flying fuck about a game that offends Christianity!?". Of course they fucking do
3DS units sold (millions):
North America: 5, Europe: 5.18, Japan: 7.23 Other: 1.39 .
Oh yeah, you're right, Nintendo totally don't give a shit about those 5 million Americans and 5.18 million Europeans, the majority of which are Christian. Especially when this whole game isn't in Japanese, it's in English. And guess where western indie games get the vast majority of their revenue? That's right, the west. Indie games do well because the indie games scene at the core are close knit and supportive, and then they spread that to a wider audience at game release. The indie games scene isn't big in Japan, because it's so dominated by western devs, so they don't have that close knit community to show it to the masses. All they have is the games lost in the E-shop under a pile of BUY OUR NES VC GAMES, WE GET TO KEEP 100% OF THAT REVENUE, and games produced in Japan.
So, yes, when they're selling a western indie game on their console, of which the majority of purchasers are from Christian countries, with a game that only a tiny minority of buyers will be from Japan, after a tough 3DS launch, you can bet your ass they care, especially when their image is of a family friendly company.