It's already been stated but I'll just elaborate on it a little. It is very likely that Godbert didn't veto the Doman refugees out of malice intent, but because it was for a greater good (both for Ul'dah and for them). Current Ul'dah is wracked with criminal activity from the Ala Mhigan refugees who feel entitled, there is a massive class divide in their society between Upper Class, Lower Class, and Refugees, adding more refugees would only cause further divide and perhaps a secondary refugee class as the Ala Mhigan and Doman fought for scraps.
In essence, life for the Domans in Ul'dah could have possibly been worse than life under the rule of Garlemald back in Othard, and Godbert spared them that with their vote hoping that they would find better shelter elsewhere. Ul'dah is falling apart currently, they can't even maintain their current population of refugees, taking on more would have likely caused the city to just crumble.
In essence, life for the Domans in Ul'dah could have possibly been worse than life under the rule of Garlemald back in Othard, and Godbert spared them that with their vote hoping that they would find better shelter elsewhere. Ul'dah is falling apart currently, they can't even maintain their current population of refugees, taking on more would have likely caused the city to just crumble.