I was increasing the MTU on an SFP interface on a CCR1036-12G-4S running v6.37.4. That SFP interface was attached to an ISP circuit that was not being used at the time, but the interface was up. Shortly after applying the change, winbox exited. After reconnecting, it appeared that the approximately 2000 PPPoE sessions (Connecting from multiple different interfaces) were disconnecting. It was difficult to stay connected, though I used the command line to revert my MTU change and things appeared to go back to normal after a few moments.

I'm trying to figure out what happened exactly... Is there any property of the CCR routers that can cause disconnections or other temporary network interruptions to multiple interfaces while applying changes to other "unrelated" interfaces? In my mind, the MTU change should have only caused temporary issues with the one interface I was configuring, but instead it caused disconnections across what appeared to be all interfaces.

Humm, Interesting!! Did you do that on your main LNS during your regular business hours by any chance??

Thank you
Regards

Is there any property of the CCR routers that can cause disconnections or other temporary network interruptions to multiple interfaces while applying changes to other "unrelated" interfaces

Yes, sort of: the use of "masquerade" action in NAT can cause this.
Especially when there are quite a lot of pseudo-interfaces.
Don't use masquerade, use src-nat.