What the passive-interface does for OSPF is to supress sending OSPF packets out that interface but allows advertising the subnet of that interface out the other OSPF interfaces. It is appropriate to apply passive-interface on interfaces for which there is no OSPF device with which you need to communicate.
There is not an exactly equivalent command for HSRP. If there were a command that suppressed sending the HSRP packets then HSRP could not work. If you are really concerned about this, then it becomes a motivator to upgrade the code to something that supports more secure authentication.
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...