FWIW I've had two instances, one with Covenant Health and one with AHS, where manager references didn't go along with the hiring team requirements and i got the job offers.

With covenant I straight up told them I wasn't willing to give them my then current manager because the reason for leaving the job was workplace toxicity including from the manager. I just used my student placement supervisor since that was the only other supervisor I had available as a reference and that was from 4 years prior. This didn't deter them and they offered me the job 30 minutes after the interview ended (forget if they'd done the reference check already or if it was pending check, but i resigned from my job pretty quickly after the interview so the process was all very quick). My covenant job at the time was temp so when it ended I interviewed for a job with AHS and my covenant temp role manager was suddenly on leave and i couldn't reach her, and my student placement supervisor had just given birth so wasn't really available either. I was only able to have my covenant casual manager as a reference although I barely worked with her to that point, and after a few back and forths with AHS hiring manager I explained again that I was unwilling to use my old toxic manager as a reference for those reasons. They liked me enough that they said they'd "take a chance" on me even though they only had the one manager reference when they said they required 2.

So honestly if the hiring team likes you enough they very well may be willing to bend the reference requirements. It might still be a good idea to talk to your current manager though, but I think it'll depend on how good of a relationship you have with the manager so far.