not relying on google services to run

There's no compelling reason to put 1Password on F-Droid as it's a closed source password manager. I goes against the F-Droid philosophy to me. If you run DivestOS, you have to accept that it is strongly geared towards FOSS as their website says. In that case, you can totally use another password manager like KeepassDX with Syncthing or Bitwarden.

I noticed you used the word security, but in fact it seems you also mean privacy. flashing a custom rom on a phone that can't relock its bootloader if it's not the factory rom is actually less secure. Only exception I know is GrapheneOS on Pixel phones because you can relock the bootloader easily without bricking the phone. That's possibly the most secure and privacy oriented phone os. When you go this way, you can expect to only use FOSS apps. It would defeat the purpose of those privacy/security focused roms otherwise. That's my point of view at least.

I run LineageOS for MicroG because I use some apps that require some form of Google services support even if it's not the official Google Services and I did it for privacy reasons, to get rid of my Google accounts for instance. 1Password does work there. Interestingly AuroraStore reports that 1Password has zero trackers, not so common for closed source apps.