It is safe to eat dyed Easter eggs.
Easter egg dye is safe and non toxic although you would peel away the Easter egg shell before eating the hard boiled egg.
Myself and my kids as well as many other kids and adults have eaten dyed Easter eggs for years without issues.
Just peel off the eggshell and throw the eggshell away and then eat the hard boiled egg portion.
Even if the hard boiled egg itself on the inside got some Easter egg dye on it there is nothing toxic about it and it's safe to ingest.
Easter eggs are safe if handled properly.
Whether using hard cooked eggs for dyeing, decorating, or hunting, they must not be out of the refrigerator for more than 2 hours.
Hard boiled eggs are safe to eat as long as they have not been out of the refrigerator longer than 2 hours.
So you should hard boil the eggs and then cool them off and refrigerate them before being ready to dye them and then have the Easter egg hunt soon enough so that they are not out of the refrigerator longer than 2 hours.