I’d be OK with 1Password, and would prefer it over Lastpass. I’ve used it as my main password manager for the last few years, until recently.
If we haven’t, I’d consider like us to consider using Bitwarden. It’s open source and I personally switched from 1Password to it once 1Password started to push for cloud/subscription/whatever only model. So far so good, and I know a bunch of other people use it at Status too (@arnetheduck IIRC?). It seems to align more philosophically with us as well. It has a reasonable iOS app and extensions you’d expect.
They seem to support teams: https://blog.bitwarden.com/password-sharing-is-here-organizations-cf9e7a2098d2 but I haven’t tried that part of them, nor have I evaluated our requirements thoroughly compared to Lastpass/1Password. See more here https://bitwarden.com/