Why jeopardize their positions in society by screwing with the Chantry and Templar Order? That would definitely be baiting an Exalted March on Nevarra, and since their organization is already a source of controversy within their own country, you can bet the nobility would throw them under the bus in order to avoid that.
Oh, well, I'm an activist Mortalitasi and would take the risk. 
And about an Exalted March against Nevarra, I'd see that being Orlais vs. Nevarra in the end, which isn't too far off anyway if a few signs here and there are to be taken seriously, and Nevarra could win, especially now against civil-war torn Orlais and their shambled Chantry. If I understand correctly, the core forces of an Exalted March are mundane armies, and I don't see other nations volunteering to make war on Nevarra to Orlesian gain.
And I'm not certain that they're actually controversial as an order within Nevarra. Outside, yes, but inside WoT says they're respected and doesn't really say anything else. They seem controversial at the moment arguably only because the king's opponents are using them as an excuse to discredit him.