I don’t think you should assume it’s limited to Americans or that it is always religion based.
For me, if you implant something in the body what is the risk of a bad reaction?
Second, how do you remove it, or is it even removable? Take the notion of implantable long-term birth control - fine, you implant these things under the skin. When they’re done, how do you get them out? Or don’t you? Is a woman throughout her reproductive years expected to accumulate eternal lumps on her arm(s) that remain the rest of her life? If it has to be surgically removed how much scarring is the result? And is a woman just supposed to put up with repeated slicing up of her arm(s) as part of her reproductive life? Or was this thought up by people who gave no considerations whatsoever to the matter? (Note: I am aware of how this is handled with Norplant, consider this an idealized example of the questions involved).
RFID chip in the hand? I’ve heard about these being promoted as, for example, a work ID that lets people in and out of secure areas, acts as a timeclock, etc. OK, fine - when your employment ends will that former employer pay to have that lump removed from your hand, or do you simply retain that lump forever more? Given how people move from job to job does that mean your hand(s) are repeatedly injected with every employer’s own chip? Wow, that could be a LOT of lumps. At what point does that start to risk impairment of your manual dexterity? What about infections, who pays for that? Your current employer? What if it’s from a chip from four jobs ago and your current employer says it’s not our problem?
Interfaces between your brain and machinery? OK - what happens if your interface gets hacked? There’s already a problem with implantable defibrillators and heart pacemakers that can be hacked, that’s a real-world problem and not a hypothetical future one (although it hasn’t become a major crisis… yet)
None of those concerns are religion based. I do think there should be an answer for them before these additions to humans become mandatory.