What a bunch of bullspit. If you are balanced and light while riding, no matter what discipline you are doing, then doing more disciplines that are different will, like DR said, make you a well rounded rider...and a better rider.
If you can ride your barrel horses with the same finesse and discipline as you do with your dressage horses, it will make you a better horsemen and you'll always have better horses. If you can sit a hard rate and turn on a good barrel horse, it will make the jumping seem easier, even if a horse refuses.
Every moment you spend on a horse, if you are attentive to what you are doing, will make you a better rider. How many strict dressage riders do you think could go and successfully run a barrel pattern, even on a made horse? How many of those yank-n-kick barrel racers would be able to ride a dressage horse of any caliber?
The more you do
with horses, the more you learn
to do, and if you do it often and keep attention on the details, you'll get better in every aspect.