My mother tells the story of her father, who was a commercial fisherman on the Mississippi River. The cleanings of the day's catfish catch went into the pen of broilers they were raising, which really cut their feed bill and provided plenty of protien.
However, when the birds were roasted later, the whole house would smell of fish instead of chicken! They would sit down to the meal and the chicken would taste like fish!
Now, my mom admits they sold some of these broilers to a neighbor who didn't notice any of this, so it might have been just a thing in their own house or family.
But still...
Most things in moderation are probably acceptable.
The cost effective thing is to find a protein source that makes sense in your area and use it in wisely. Fish on the coast and along the rivers makes a lot of sense, in moderation.
I am not opposed to using mammal protein myself in moderate amounts, as birds have been scavengers of that kind of meat for a very long time (and I cannot prevent them from hunting and eating mice).
I would prefer to feed them invertebrates, but if I start growing bugs for the chickens my DH will have me institutionalized.
And yes, the birds get anything freezer burned. The medical doctor told me freezer burn does not indicate bacteria or spoilage, just a texture change that people usually find offensive. The birds do not seem to care.