What are some specific reasons NOT to share a users database table between sites?
Almost any problem you see will be similar to content cache problems on a Drupal site.

The database represents your site's canonical state. Sharing a user table between 2 different sites means canonical user data reads/write can become invalid without each site knowing it, since they aren't coordinating their actions. 

For example, Site A is doing a bulk operation (e.g. add Role X to all selected users) on users. It loads all users from a DB query into memory, changes a property on each user object, then executes a save to the DB. Meanwhile, Site B has a user who wants to update his email. He visits his user page, updates his email only to see it change back a few minutes later because Site A, still working through its bulk operation, has an old version of the user account and saved it after he updated his email.

Depending on the size of your site, just like with content caching, this invalid state problem might never show up. If Site A &amp; B represent 2 different sub-sections (e.g. a blog site &amp; commerce site) with users seldom using both, the scenario where the user state becoming invalid might never happen. But as your site grows (i.e. the number of user DB transactions) this invalid state problem will likely show up eventually.