Apple Mail - Do not apply rules automatically
Solution 1:
Apple Mail rules run automatically only the first time they're set. After that rules will only run manually.
Going into Preferences and unchecking 'Active' will deactivate the rule and will never run it.
Solution 2:
In Apple Mail, go into the Preferences and uncheck the "Active" box next to your rules. Then they won't be run automatically. They will be run if you manually select Apply Rules.
If you want some rules to run automatically and others only to be manual, you need to do a couple of extra steps. First, move your manual-only rules to the top of your list of rules, because rules are applied in the order that they're displayed in that list. Then, in your manual-only rules, make sure that the last item under "perform these actions" is "stop evaluating rules.