How does accepting military aid request from ally affect reputation?

If you are on perfect terms with an ally (ie have military access and a marriage alliance) and this ally asks you for military help (ie to wage war on) another faction that you are NOT allied with (in fact that you have terrible relations with), but have trade rights with - will this cause your reputation to decrease?

Here's my situation - as Hungary I have been allied with the Poles for about 50 turns now. I have a marriage alliance, as well as trade rights and reciprocal military access. I give them my map every few turns to "manage" the alliance. I was recently "invited" by them to join in their war against Milan, who I have terrible relations with but have trade rights with.

I ended up not accepting the offer as it wasn't in my best interests, but am curious - had I accepted would it have affected my reputation?

I've been in quite the same situation exactly, but with the Byzantines instead of the Poles and the Turks in place of Milan... I myself accepted to assist in the attack and took place with one of my stacks in one of the Byzantine battle against the Turks... My overall reputation took no hit...(maybe the fact it was a muslim faction helped) but I gained no thing from the Byzantines either, my standing stayed on Very Good...

On your situation, the only consequence to your reputation might be with the Pope who might not take lightly your joint attack on Milan (catholic)... But if you grease his palm sufficientl, you should be OK...

I don't think violating trade rights results in any reputation penalty; I think that is reserved for alliances. Your rep with the faction in question (Milan, in your example) will most certainly get penalized, but overall I don't think there is any damage done.

Yeah, the money-grubbing Pope may not like the situation, but give him a few bucks and he'll love you and let you invade whomever you desire.

Well, as far as I can judge, you do take a reputation hit for attacking a faction even if you´re neutral with it (i.e. not allied, only trade rights, but maybe even attacking a faction you´ve got trade rights with carries a more severe penalty than attacking just a neutral faction), but this goes for "uncalled for aggression", i.e. an attack out of the blue. If, however, you assist an ally, you should be seen as trustworthy (especially if you actually agreed to assist your ally), however, whether the game mechanics share this point of view I have no clue.

As a matter of fact, even an attack after the diplomatic message "accept or we will attack" should increase your credibility - you´re a man of your word. Again, however, I doubt the game works this way.

Trade rights is a treaty, as such I expect it is treated like the other treaties. I expect you will take a reputation hit for breaking that treaty. This is easy to find out. I'll have a look & report back, if anyone already has the figure -> fire away !

Even though it doesn't really makes that much sense, I believe that you will lose reputation merely because you are the one declaring war and hence, you are the aggressor of the conflict