I'm sure you can, but knowing how conjunctivitis can make people feel uncomfortable or miserable, i don't think I would do, personally. Presumably you're treating it so hopefully it will clear up in a few days.
Mine went through a run of this a few years back and at this time of the year I really needed to keep a fly mask on her so they didn't get attracted to all the gunk - so no riding. Plus she kept trying to itch her eyes so masks on 24:7 with regular changes to a clean one was needed.
I do remember lunging her early in the morning while it was cool and no flies but that was mainly because she was fat and needed to do 'something'. I suppose technically you could ride, but I think you'd just find the flies turn up and the horse gets upset