There was a Butcher on Long Island called Commack Kosher Butcher who has a conservative Rabbi as supervision. At the tine ny had a kosher law and the butcher was fined because they did not meet the orthodox requiremts. They sued based on they had conservative supervision and the law was declared un constitutional.
comments on some blog arent going to get you sued, but if someone local orthodox rabbi declared publically not to buy from a place with conservative supervision, the owner might have grounds for libel.