Not anymore, iOS 13+ allows background nfc reading on the iPhone XR and up
In your line of work, I have a feeling you really shouldn’t. For one thing, you couldn’t approach a MRI machine anymore. That would make parts of your workplace off-limit for you. Not a great career move I would think 
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I rarely work with MRI machines. I have had more done to me in 5 years than I have been around with patients. I would just tape my finger up before I went in.
I doubt it would rip out. I almost promise it would be uncomfortable though.
I also wouldn’t tell my employer
There have been anecdotes where small mags like the m31 felt painful but could be held or taped, but a couple people have tried enduring larger ones and could not complete the procedure… but of course… anecdotes.
Also another anecdote - supposedly there are locations in 3D space and associated angles at which you can hold magnets while entering an MRI that sort of negate the pull. No idea if that’s even possible, but ok.
It doesn’t sound like you’re really in that situation, but I know if anything you do has any chance of interfering with your work duties and you don’t inform your employer, that’s ground for termination when an issue comes up. In your case, you may not work very often with MRI machines, but the day someone asks you to go in there and do something, and you tell them you can’t, you might have a problem.
Another issue I can think of: imagine some idiot patient learns that you have an implant and complains that you “magnetized” their blood sample and skewed their results. You and I know it’s impossible and plain mumbo-jumbo, but you might be called in your supervisor’s office to explain yourself, and they might decide to let you go following the precautionary principle. You’d be surprised how irrationally companies can behave when it comes to avoiding lawsuits. It’s not very likely, but I bet it could happen.
There was a guy who worked as a machine tool operator for years in the factory I worked for years ago. One day his shift manager discovered he was color-blind because he mistook one red light for a green light, and fortunately the machine went into alarm just in time before the headstock caught onto his sleeve. He got the sack for failing to mention it during his interview, and so did the company doctor who failed to test him at each checkup.
Me, I don’t work with anything dangerous. But I do disclose anything I undertake that I reckon has even a remote chance of creating an issue at work. At least if something does happen, it’s on record, and the onus is on my employer if they failed to take appropriate actions.