With SQL transactional replication, does changing user permissions to a table trigger a new snapshot?
If you change a user's permissions to a particular table BEFORE a Subscriber has been initialized or reinitialized, if the article property Copy permissions is set to true, the permissions will be copied to the Subscriber when the snapshot is applied.

If you change a user's permissions to a particular table AFTER a Subscriber has been initialized, the permissions will not be replicated on the fly, unless you generate a new snapshot and mark the Subscriber for reinitialization.  Note that the article property Copy permissions must be set to true.

What is typically done is if you need to change a user's permissions to a particular table AFTER a Subscriber has been initialized, and you need the permissions to be present at the Subscriber without reinitializing the Subscriber, the script to grant permissions are posted to the Subscriber using sp_addscriptexec.

I have a post detailing sp_addscriptexec located here at Executing scripts with sp_addscriptexec.