Well, most martial arts involve some sort of contact, unless we're talking about weapons or taiji for health. Aikido certainly requires some contact unless we're doing "no touch" throws.
Whether that's "necessary" or not is the precise issue. I don't think you can learn aikido without some contact. And by extension, what is the point of learning a semi-contact martial art then if one's religious beliefs deems it "unnecessary"?
For starters, I don't think the religious beliefs issue should be brought into the dojo. It should be left outside the door, together with one's shoes and ego. If one cannot relinquish any of the above, then they should remain outside the dojo where they would be more comfortable in their own insular world.