"As long as you don't use +p or "hot" loads it will be fine."
Uhm... .357 Magnum loads don't have +P rankings... They're magnums, which are, by definition, hot.
"Most folks I know that own Uberti model 1873's are using them for CAS events and mainly shoot mild loads through them"
I think the primary reason CAS shooters shoot mild loads is the quest for speed combined with accuracy, not because they're afraid of damaging their rifles.
The 1873's toggle design isn't the strongest, that's well known, but I would think that one manufactured with modern steels would be a lot more durable and able to handle higher pressure cartridges than one made with the soft steels and cast iron of 130 years ago.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.