EtBr is a DNA intercalation agent. I mean that EtBr alter DNA structzre, There is no direct evidence that EtBr is a mutagen, but some EtBr derivates can serve a s mutagne, There are also no direct evidence that EtBr is a direct cancerogen. However, it is obviuos that one need to work with EtBr with high care
The problem with alternative EtBr dyes is that sensitivity is different. 1ug of DNA ladder with EtBr runs fine on an agarose gel whereas 1ug of the same ladder looks smeary and ugly with sybr. Same applies to DNA and RNA...you have to run less to get the same image quality.
Effect of EtBr on mitochondrial DNA is used in veterinary medicine to treat trypanosomosis in cattle, as EtBr binds molecules of kinetoplastid DNA and changes their conformation to Z-DNA form. This form inhibits replication of kinetoplastid DNA which is for trypanosomas lethal.