In general, training while sore is perfectly fine and usually beneficial, subject to a few caveats discussed below. Almost every serious athlete frequently trains while still a bit sore from the previous workout.
you are correct no stretching is going to solve or prevent DOMS due to the definition of DOMS and I never said that. My statement was stretching can help stiffness and soreness and it does. I dont have a problem with DOMS because I'm careful and follow rules such as 'stagered workouts' and proper recovery times. Article abount DOMS:
I would say it isn't a good idea to do heavy training consecutively on the same muscle group.
sometimes when you're starting out a new exercise like a cardio routine your muscles can get sore because they're not used to being worked. In that case I would say that it would be just fine (with moderation).
Either way you need to let your muscles recover properly and it's a good idea to change up your routine day-to-day or to have a staggered schedule.
In any case, overworking can hurt your results.
The second thing to understand is that soreness has nothing to do with the effectiveness of your workout. It's more of a side effect, which is actually not well understood. Depending on your training level and workouts, you may still be sore even when your muscles are in the supercompensation period. If this happens, you just need to put up with it and train sufficiently hard to keep the gains coming.
BTW, this is also a reason why split routines - where you train each muscle once a week - are very inefficient for the vast majority of beginner & intermediate lifters. Your muscles hit the supercompensation period in far less than a week and have started to return to normal by the time you train again. In this respect, fully body routines 2-3 times per week are going to produce strength gains much faster.