I think red mites are bad. Was reading something about that earlier this week. Yeah white and brown mites just compete for food with the worms but red are blood suckers. To prevent you need to keep your PH value at neutral or above. To do this you need to watch your moisture levels, keep them below 85% and adding some calcium carbonate as needed. thats all that it said to do, but it was talking about prevention.

Removing the food shouldn't hurt anything. The red mites might be there because of the dead worms and not the other way I don't know anything about them. You didn't say anything about the kind or size of the bed but you might start some new bedding (wet newspaper strips,) for them with just a little ground up cantalope or pumpkin to keep them going. Put it over to one side and hope the worms move into it and take out the old bedding as they do.