1) I don't really think this was "overtly Anti-Christian", however:
You don't actually have to specify which group you're talking about for it to be obvious who you're talking about. Randall wasn't talking about the Hindu version of Re-incarnation. He just wasn't. If I start making jokes about unemployment, the ability to play basketball, dancing, being at the back of the bus and liking watermelon, it is obvious I am referencing certain stereotypes. It is hugely unlikely to be true that "I'M not making a stereotype! I could be talking about ANYBODY, YOU'RE the one who made the stereotype". Especially if those stereotypes are a big deal in the speaker's culture.
The chance he was specifically referencing the Bahai/Muslim/Hindu version of events is similarly extremely low in my opinion, about as low as the idea that I was referencing Israeli women above (which could be stretched to fit).
2) This doesn't actually make much sense without the Christian reference. Without the reference to say, a soul, the body is still intact on death. The arrangement is unchanged, therefore it is only when you take the pieces apart that it is no longer Grandpa. (There is an obvious counterpoint here w/r decay, but then we move on to point 3).
3) The human body regenerates cells, hair, skin layers, etc. all the time. The only part really staying put in any real sense is the teeth and bones, not counting the atomic level.
Therefore: He does seem to be suggesting that Organ donation is somehow stoppered when it comes to thinking about a soul, which it just isn't. Major religions around the world not only allow, but in most cases encourage organ donations. (Anglican says it is a religious duty, Catholics advise it as an act of charity, Muslims are in favor, Judaism is the same). This is what I think one of the first posters was talking about when he called it Anti-Christian.
The end girl seems like her belief in a soul made her choose not to donate organs. I think this is unfair, the only difference is, I don't think it was an intentional jab at religious folk so much as it is more like some of the passive racist comments I hear from time to time.
Example, I once showed an aunt some home video of the middle east where some Arab family and friends were sitting around at a barbecue. She responded with "Oh look, they're sitting around and eating and smiling just like normal people, that's great". She didn't try to insult anyone, and in fact was trying to be nice. Yet the implications of what she is saying is that her expectations were that those Arabs were sub human, at least before seeing the video. "Arabs don't sit around smiling, eating, playing football in the park and talking".
It isn't a big jump to guess what she expected Arabs to be.
4) Off track a little. Therefore I think the comic's priori and conclusion don't really match. They're all very very loosely tied together with vague references that don't really make much sense when looked at in any level of detail.
5) Sorry fanboys/girls. Don't kill me.