I will ask through an illustrative example:
Say I play Robin Hood, who has the faction Band of Merry Men. Robin Hood admits Little John to the faction as matter of course. Later, Robin Hood is approached by Will Scarlet, who asks to join the Band of Merry Men as well. Say that Little John and Will Scarlet are played by the same person. Obviously, this is stream-crossing; their player shouldn't be doing this.
If I know that Little John and Will Scarlet are both played by the same person beforehand, is it my responsibility to have Robin Hood come up with an excuse to refuse to admit Will Scarlet while Little John still exists in the faction? If I learn that Little John and Will Scarlet are played by the same person after they are both admitted to the faction, am I required to have Robin Hood give an IC reason to remove one of them, or should I simply mechanically remove one of them as quickly as possible? Is it my responsibility to communicate through some OOC means (Discord, tells, etc.) to ask the player to choose which of their characters they want to stay in the faction?
Or is this something that, mechanically, DMs can detect, so I should just allow the roleplay to emerge naturally - permitting Will Scarlet to join and trusting that the DM team will sort it out?