That's a good question. I eat them, based on the testing data, not the history or rumors. Unlike many waters in Utah, UL
Does Not have a problem with Mercury. The advisories for the lake are related to organic chemicals called PCB's. That is good news because Mercury gets into the muscle tissue and can't be reduced by proper cleaning. PCB's are fat soluble and end up mostly in the fatty tissue.
Because of that, you can fillet a small or medium sized cat, then remove the fatty tissue along the lateral line and have a fish that does not have enough residual contamination to warrant and advisory.
The fish that have tested above the advisory level are the carp and the cats. As WH2 said, the panfish are generally fine.
Here is a graph showing comparisons to the EPA and FDA advisory levels from testing in the early 2000's
The noteworthy point in this graph is that you can buy salmon in the market that have nearly the same level of PCB's as the cats in UL, because the markets are governed by the FDA limits, not the EPA advisory levels.
And another graph showing how the contamination levels are reduced if you fillet the fish and remove much of the fat soluble PCB's
If you want to read the report I got these from, send me a PM and I'll forward it.
The longer a fish is in the lake the higher the level of contaminant. So I limit catfish consumption to those less than 24" long.
Enjoy!