Risks of changing to ARITHABORT ON
So SET ARITHABORT ON basically says "if a divide by zero error happens or an arithmetic overflow happens abort the query" This is usually desirable behavior and is the default instance wide setting. If this causes issues with your vendor's queries, I would say that they may have been suffering from some coding issues to begin with. I would ask them for more details on why they are concerned here.

Of all of the rules of indexed views, I would call this and many of the set options rules the least controversial. 

This would have to be set in the connections that interact with the view. So you would want to work with the vendor and really try and understand their reasoning and try and get them to commit to what they are thinking on the big disagreement here.

That said - Indexed views are a bit of a big deal. They have other rules and they can impact the application and assumptions the vendor's developers had when building and performance testing. You should really have a conversation with them about the business problem you are trying to solve through indexed views and get them involved in the conversation about how to solve the problem.