One gmail account for a church and its school, or two?

Two addresses, honestly. One address with two signatures gets messy fast, parents of pupils end up seeing church newsletters. Make a school address and a church address, then instead of sharing passwords, in each one's Gmail settings use Accounts > Grant access to your account to add the volunteers as delegates. They see the inbox from their own login and you can remove a delegate when someone leaves. Also check whether the church qualifies for Google for Nonprofits, it gives a proper Workspace with shared inboxes at no cost.