Clarity uses the same hybrid system as the Accord hybrid and the Insight, so there is no reason any dealer can't service them, but if one refuses then you wouldn't want to take it there anyway if that's their attitude. Dealers mostly make money on service not sales, so if they don't want your business you go somewhere else, although that could mean a longer drive unfortunately.
Some people worry that mechanics won't be able to work on it if they have never seen one before, but it's no different than when a new model of any type comes out, or even a popular model that has an uncommon problem that the mechanic has never seen, they are provided detailed instructions to follow. They do need training on hybrid systems but again they likely already have had that training for the Accord and Insight. It may in some cases however take them longer depending on what the problem is compared to say an Accord or Civic, and also parts might take longer to get.