What is the legislative status of the dua after the prayer, doing it regularly and doing it in congregation? And can it be a cause in separation between the Muslims?

Making dua after the prayer is legislated, but not in congregation, in fact everyone should make dua [on his own] for himself and for the Muslims. He should not raise his voice with it or disturb others [by doing so]. Allah, the Mighty and Majestic said: “When you have finished the prayer, remember Allah standing, sitting down and lying down on your sides” [Nisaa 4:103]