Multiple Replacement Effects for "Next Time"
The Dragon-Style Twins will not deal damage in either combat damage step.

One of the subrules of the rule you quoted, 616.1e, says


  Once the chosen effect has been applied, this process is repeated (taking into account only replacement or prevention effects that would now be applicable) until there are no more left to apply.


So, in the first combat damage step, the process of applying replacement and prevention effects goes like this:


We start with two instances of "the next time Dragon-Style Twins would deal damage to you this turn, prevent that damage".
The effect to be modified is "Dragon-Style Twins deals 3 damage to you".
You choose (arbitrarily) to apply the first prevention effect.
The new effect is "Nothing happens". Now there are no applicable replacement or prevention effects, so the process ends.
One instance of the Circle of Protection: Red effect was applied, and the other was not, so now we have one remaining Circle of Protection: Red effect to apply.


In other words, a replacement or prevention effect that applies to "the next time" something would happen is only consumed if it is actually applied to an event.