No, it isn't reasonable and I don't care on an interpersonal level what you do as an individual, I only care about policies informing me on what I can expect in communal spaces.

As more businesses, employers, and institutions arrive at policies one way or the other regarding the vaccine, then you can make a personal decision about what to do about that. No, you will not be able to raise any random objection and override the entire enterprise. It doesn't and can't work that way.