AlterBrains

If you are logged into a master site, could you complete a subscription form on a slave site as a new user without sharing the session data across the two sites? Basically, the slave site would just see the logged in user of the master site as a new site visitor. This would allow the logged in user to create a shared subscriber across the two sites.

Sorry, I don't understand you
User can be logged in master site and not logged in slave site (default behavior).

Sorry about the confusion,

So If I'm logged into the master site then, I can register a new user account on one the slaves site without the slave site inheriting information from the master and sharing the session data? Essentially, I would be subscribing/creating a new shared user on the slave site while still logged into the master site.

Yes, you can be logged in master site, next go to slave site - you will be not logged here, so you can register as usual.
Note that if slave site shares users - you can register with same username / email as you have in master site.