It depends what state and area you are in. In some states or localities, it's illegal to sell alcohol that isn't "properly" labeled with the correct name of the brewery, and the product inside.
You can decide to not go to a brewery that refuses to fill another's growler, but you might have to not go to any breweries in the state of Michigan, or other states.
Anyway, to answer the question asked, many growlers are not designed to hold the carbonation pressure, and are only safe to serve carbonated beer in once it's dispensed. We've seen lots of exploded growler photos on this forum, those of us who have been around for a while.
I use growlers occasionally to take beer out of the my home, but I never carbonate in them. If you choose to, just put them someplace safe just in case.