I'm new to this quest, so I don't know exactly how this QM runs things, but every quest I've ever been in had consequences to choices that weren't explicitly laid out in the question. Probably because that's how real life works.
There will be plenty of unforeseen consequences, but those are long term, not immediate, and caused by how we choose to act in future votes.
This is a faction pick between the three main groups at the court, and has been pretty explicitly given with clear consequences so people can make their choice without fear of unforeseen consequences.
This quest has no trap options, usually if there is uncertainty of outcome, we will either be given the DC of diceroll, or not told the consequences, this vote is not one of those.
Consequences are as follows, two clans will like us more, one clan will like us less. Shenhua is almost certainly not going to change their opinion no matter the option picked.
edit-
I still think the military option is the best. at most we annoy the meng a bit, but they are hardly connected to ling qi. we bond with the wang which we already started to of course. on top of that all, it makes sense because of the war context. this seems like the safest option.
sorry for pointing out the maybe obvious.
We were brought in to build bridges with the traditionalists, which include the Meng, and happily picking culture option will not annoy Wang either so that's a pretty safe pick.
Pick military and you will annoy the traditionalists, pick traditionalists you annoy merchants, pick merchants and you annoy the military.
Except in 2 to 1 ratio, so you always end up 1 up in relations.
Picking culture you gain rep with the faction we were supposed to help the Cai with, and don't annoy the people we are currently working with, nor the merchant clan whose scion is courting us (and also one of who is kinda sorta not really but actually dating Meizhen, so that's a reason to stay nice with the Bao).
Also getting good with the Luo might help with the Bao/Luo issue at the sect in a way that leaves Meizhen happy and us with a new crafter friend while not pissing the Luo.