Comment 17 for bug 1784774

I did some more investigating, and I think there are two independent problems here:
(1) The problem as believed so far, network access permissions
(2) New insight: Kerberos doesn't work with snaps.
This explains why fixing (1) didn't help me (or Adam).

Background: Kerberos is the authentication mechanism used for NFS. Assuming you are using authentication (as almost everyone does), then when you access NFS contents, you need to provide kerberos credentials. These are stored outside of your home directory (after all, home directories are one of the most common reasons to use NFS, so you can't store them there). I believe snaps restrict access to just your home directory, so you can't access the Kerberos key and therefore can't access your home directory.

This is supported by various bugs like https://bugs.launchpad.net/ubuntu/+source/chromium-browser/+bug/1849346 (unresolved) which is a different but relevant issue - people who don't use NFS but do use Kerberos features in Firefox found they don't work post snap conversion.