I think it depends on the nature of the game, and the nature of the mods.

Ultimately it boils down to the communications protocol that the network is expecting.  

If the simulation is done entirely on the server, and if the mods are entirely on the way the game is displayed, then there shouldn't be any problem.  This would be the case for see-through-wall cheats, aim-bots, and so on.  They all follow exactly the same communications protocol and the same events are always as expected.

If very much of the simulation is done on the client then there can be many compatibility problems.  They may or may not follow the same protocol based on the mods and the game details.  In that case it would be unwise generally to allow them to play on a shared server.

I think it depends on the nature of the game, and the nature of the mods.

Ultimately it boils down to the communications protocol that the network is expecting.  

If the simulation is done entirely on the server, and if the mods are entirely on the way the game is displayed, then there shouldn't be any problem.  This would be the case for see-through-wall cheats, aim-bots, and so on.  They all follow exactly the same communications protocol and the same events are always synchronized.

If the very much of the simulation is done on the client then there can be many compatibility problems.  They may or may not follow the same protocol based on the mods and the game details.  In that case it would be unwise generally to allow them to play on a shared server.