Thanks for the reply.
The conflicts are difficult to define because the logic of the situation is certainly complicated. But, basically, the modules will load correctly and look fine, but then when the user starts using the links the result get unpredictable. For instance, clicking on a link may reveal other links that are part of the second (supposedly unpublished) module only. How that can happen when the two modules have mutually exclusive assignment I do not know. There must be a conflict.
Incidentally, the conflict situation also generates a Geocode error from the Google maps module on my site. Unpublish the categories modules and the Geocode error disappears! Wow - it drives me mad! I am tempted to conclude that I am trying to achieve the impossible.
Actually, all I am trying to do is as follows. I have two categories of product. I want non-logged-in visitors to see only one of the categories. Logged-in visitors should see both categories. It sounds simple doesn't it?! I started out with shopper groups and this worked basically, but of course left the forbidden categories displayed with no products. Also, for non-logged-in guests, the categories module displayed the forbidden categories avaiable only to logged-in guests!
There must be a simpler way of doing all this.