My experience generally is that avoiding both Google and Apple is pretty difficult. I've been running both un-googled android and trying out the pinephone, and while it's generally been technically feasible to run BankID together with microG, it's definitely not officially supported, which you'll notice immediately as there's no official way to download the BankID apk. I also found out that setting up an new ID isn't currently working with microG when I bought a new phone a few weeks ago, so I'm still stuck with the old one for now.
I'm also kind of at a loss for how to work this situation, living without Swish and BankId is certainly possible, but it's incredibly impractical, and continuously getting harder. I think we should be allowed to choose whether to agree to contracts written up by private companies, but most people don't seem to care.