So....when the apostles asked Christ how they should pray...Christ sat down and recited the Lord's Prayer.
Christ didn't tell them to not pray, unless they were "with their own kind". In fact, when Christ uttered the prayer, I bet there were non-believers present.
The danger of praying with others....isn't so much praying "with" others, as it is growing to "accept" that the others might have a grain of truth, or be fine the way they are...or perhaps even the weak believer might find them more interesting and leave the Church....in addition, to giving the "others" a semblance of credibility for joining them in prayer to their false deity, etc.
In other words, don't pray with a Muslim before they break their fast on Ramadan, because by joining, you are stating that their God is your God...which is not true.
Certainly, don't pray with Hindus or Buddhists, etc. ....but, feel free to pray for them.
However, if you are praying with other jurisdictions of Orthodoxy, old calendar, new calendar, OO, etc....this shouldn't be as problematic....as we do all serve the same God, we merely have administrative, clerical issues, as well as dogma that needs to be worked out...and by joining our brothers we stand a chance of helping them, without losing ourselves.
Praying with a "new" calendar parish, isn't going to make me want to leave my "old" calendar church....but, it will unite both parishes as one family...which they truly are.