Separate fork sync from merge by PR in branch permissions

My team has a parent repository with common code that is shared by 4 forked children. We recently implemented branch permissions on the forked children so that edits can only be made via a merged pull request. What this means in practice is we are inhibited from syncing the parent repository to the forked repositories. Instead, we had to give a team member write access directly to the main branch of the forked repository, which defeats the purpose of branch permissions.

The idea is therefore to separate permissions into merge by PR and syncing, so that I may sync from the parent but cannot otherwise edit the branch directly.