How do I stop the new "Security Notifications" that civi pops up for upgrades
Disabling security notifications hides the notice from your users, but it won't hide your sites from attackers. Turning off the warning supports a scenario where those sites are at risk longer.

Here's how we handle it for our hosting clients -


Create a recurring item in your calendar for the CiviCRM security release dates, first and third Wednesday each month. (We do the same for Drupal security releases.)
Be subscribed to the CiviCRM Security Advisories announce list.
If a release occurs on that date, run the upgrade through your testing, then deploy/apply to production.


Since CiviCRM stores personal data, I believe every organisation using CiviCRM has a responsibility to ensure there are processes in place to ensure security updates are applied promptly as part of a wider programme to protect your customers and their contacts.