When you choose to move the capital to Pentos by event after conquering Essos as Aegon the Conqueror, not only does it seem to stay de jure Pentos (which gives the local Pentos lords opinion problems with you), but the Prince of Pentos keeps his capital and title in your territory, which means he still gets his court chaplain active in your capital. That can randomly force your courtiers (or even you, the Emperor) to convert to his religion (usually Rhllor) without having any choice in the matter.