If something happened between Bandle City and one of the other states that have yordles, would they side with Bandle City or their other homes? It most likely depends on each individual case.
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If there is a war between Noxus and Bandle, 
would fight against the Noxians that are invading his land, he would also fight against the Yordles of Bandle because they are in his property... and the Ionians for no reason at all, In fact Kled would even fight against Bilgewater and Shurima at the same time for not being in the war... And then, he would go to Freljord and defeat all the queens of Freljord because he owns the place.
Kled vs the world, even himself.
My opinion is that it would depend on them as individuals and how much they regard their old home. Some of them might regularly travel between Bandle and their human nation of choice, while others might forgo that and just live among the humans for the rest of their days. It's not likely that yordles are gonna have any major conflict with humans anyway since many people haven't ever seen a yordle and actually known they have, and some don't even think they're real.
THE FLOATING NAUT IN THE BACK
I kinda figure that most humans don't even know Bandle City exists, and it may or may not even be possible to mount an attack on the city. Don't think yordles would have to choose between defending the city or fighting for their chosen faction. If it did come down to it though, what Sharjo said is probably accurate.
They would probably pic the reagion they are a part of since that is what is their home. For instance Poppy and Kled are not a part of Bandle City (for what we know). Though I don't know for sure.
Think about if you had to choose between the country you've grown up in, and the country your ancestors are from. Almost everyone would choose what they know, which is where they reside.
