Not for any reason they see fit
Their business their rules. That's why airlines and businesses can boot the unmasked, it's also why mask and vax refusing employee's can be booted. At least one of the famous qanon types who attacked the american capitol was kicked out of the American military for refusing vaccinations a decade earlier.
I've been fine. Lots of muscle strains, which could be linked given my symptoms were a week of feeling like I'd overdone it in the gym before I got actual covid symptoms. But I've bought a new place and have been landscaping the garden so shifting massive rocks could well be the cause of that.If we vaccinate people already infected/with sequelae? That hasn't even been studied. No data to go on.
Cmdr. Stigbob maybe could give a viewpoint as an example, but so far he's fine, AFAIK.
The people I know with long covid or who had covid pre-vaccine have had no vaccine related issues, other than being really pro-vaccines after infection for obvious reasons. One guy fainted immediately due to a needle phobia but a hospital is the best place to do that. Long covid sufferers get breathless easily and their SPO2 is all over the place without any warning, sometimes cripplingly so but they recover over months and it becomes less of an issue. Asthmatics seem most vulnerable to long covid. Originally I had to keep an eye on my crew mate so I could catch her if her legs went and pop her in a chair or the stretcher while her 02 stabilized, she's fully recovered now thankfully. Possible mini-stroke from covid as it affected her speech for a day while she was infected a month pre-vaccination, which is the real risk of pandemic blood clots.
No anaphylactic issues at all from any of the people or vaccination centre's that I know of either.
It's all purely anecdotal but anti-vax attitudes among us haven't survived actual contact with the virus but were fairly prevalent to a small degree in younger people who get all their news on social media and/or came from a care home background.
Care homes are the only place in the UK the government considered compulsory jabs for staff due to low take-up, again anecdotally there is a noticeable anti-vax ethos there but if you discuss it with them it's all the classic conspiracies even the autism scare yet they've never heard of Andrew Wakefield his scam or why he was stripped of his Doctorate. Again that's noticeably reducing over time, so I think direct experience of the virus is educating them.
TLDR : Covid visibly kills and really messes people up, the vaccines don't.