Praying for Nero

I have recently come across the teaching that Orthodox Christians should not pray for non-Orthodox. I cannot cite the details of who-where-when, so perhaps I am misunderstanding what is being said. But the concern to differentiate Orthodox from non-Orthodox in our intercessory prayers is real enough: I have been in one Orthodox Church where the list in the narthex on which one could write names to be prayed for in the Litany of Fervent Supplication has separate columns for Orthodox and non-Orthodox. I know of another church where some parishioners write down the names and then add “(non-Orthodox)” after them. What are we to make of this? Are there such requirements made on liturgical prayer?