I'm playing as Burgundy, trying to form the Netherlands. Utrecht has all the 4 provinces I need but is currently in the HRE. The current plan is to declare war with CB Conquest with Austria and France as allies; France is currently at war, so I'm waiting for the time being.
I'm afraid that an enlarged Brandenburg may call and join the war with a better military than me. However is is rivalled to the Palatinate, currently the Holy Roman Emperor. I'm uncertain that Brandenburg will answer the call of the Emperor while it is its rival.
Best Answer
When a non-HRE nation attacks a country whose capital is an HRE province, the emperor will be called into war. The emperor can then call their allies to war.
When you are the attacking nation, you can see if the emperor will decline or accept to be in this war, and for what reasons (relations to the battling nations, debt, war exhaustion plays into this)
So assuming you are attacking the rival of the emperor, the emperor is slightly less likely to join the war on the defending side. Keep in mind that this modifier is as far as I know less significant than the default attitude from being the emperor, meaning for the emperor to not do their job, they should need additional reasons (such as being massively in debt, being scared of the agressor)
The emperor defends (if he wants to) it's subjects, but other the subjects will not by default be called into a war, unless by another factor (such as an alliance)