It depends on the system. Some modern systems can react to high-value targets of opportunity, hunt for targets, or switch to a new target if the one they are after is destroyed before they get there. There are different variants of the weapons to deal with different use cases. The 1990s versions were relatively limited though.

Target selection is much more networked, automated, and adaptive than it used to be. Missiles can talk to each other.

I would hope it is. The fact it is even possible for a friendly system to lock onto another friendly system and fire upon it seems like a pretty big damn issue to engineer around. I guess they still haven't though considering kuwait shot down an f15 a couple months ago. You'd think lockheed or raytheon would have figured something clever out to solve this half a century ago.