Attacking hostile units which are
already within your own borders (or -- I believe -- successfully defending against enemy attacks beyond your own borders) will
never activate MPPs against you, but attacking enemy units outside your borders (including boats, unless your boats have 'Hidden Nationality') will
always do so.
So if you are already under attack, and your attacker has MPPs, and you are willing to risk 'playing the victim' for 1 interturn before making any aggressive cross-border moves, it is often a good plan to sign MPPs with his (or her) MPP-partners. The very next act of AI-aggression against you will activate those MPPs in your favour, and break all your attacker's MPPs (not to mention any other deals he/she had running with your Mutual Protectors).
And you can be sneaky too: if you want to make war without activating your target's MPPs against you, then after signing
your MPPs, to activate them all you have to do is declare/provoke your war, and then leave a cheap sacrificial unit (e.g. a Worker/Slave or Explorer) within striking-range of your soon-to-be enemy, and again wait 1 interturn. Your 'attacker' will usually be quite happy to oblige you in this, even if it does mean shooting themselves in the foot! You will(/should*) then be free to commit any cross-border acts of aggression yourself, with complete impunity.
And this way, not only does your enemy end up at the bottom of the MPP-dogpile instead of you, but your RoP-reputation stays intact, as well...
*CAVEAT: the above applies to the Epic Game -- admittedly I'm not sure if/how this trick works in conjunction with Locked Alliances, since these are only used in the Scenarios, which I mostly haven't played