We'd also have to see the full filter rule

Here you go.

You can try it yourself... email iskoch01@icloud.com.

That rule matches ALL message, but your origional post stated "I made a rule to reply to certain messages".

Are you saying this problem occurs with all rules, not just certain rules? Does it only occur for rules with action "reply with template"?

My mistake. I fixed the rule, but it still runs twice.

Thanks for the clarification.

My questions I believe are still important...

Do this problem occurs with all rules whose conditions are based on address book, not just certain rules?

Does it only occur for rules with action "reply with template"?

Also, does both the move and the reply with template actions get executed twice?

It seems that both actions execute twice, as the log file entries indicate in my OP.

Duplicate processing of other messages does not appear to occur.

I am going out of town on work today, so I'll have more log data to analyze next weekend.

You might also want to refine the filter. Sending replies to noreply address like the Firefox sign in email is probably only going to get bounces from failure to deliver.

Given the events are 2 minutes apart. Perhaps check the server web mail to see if the actually move shows up there before the event fires again. In the past I have seen instances where changes are not processed server side for some time (not apple, but still possible) Is your check for new messages set to 2 minutes?

The replies are getting sent two seconds apart. Your idea to avoid sending replies to noreply is interesting.

In case anyone else has this problem, I find that I can avoid double-replies by setting a star on the processed message. No idea why this is happening.