Q:

Adding remote site to managed package. Can we push to customers?

We will be adding a remote site to our existing managed package that currently does not have any.  We have found some documentation on the effects of such an action but we have one remaining question. Will the package still be able to be pushed or will we need to have each customer install the updated version themselves?
We have reached out to Salesforce for help with this but have found there are some discrepancies on what actually happens.
From your experience, are there any other considerations that we should know regarding adding remote sites to a managed package?

A:

After further investigation with Salesforce, adding remote site settings does not effect the ability to push to customers despite the security changes. 

