Just as a quick aside, Quickleaf: The Adventures In Middle-Earth guide actually does have disposition charts for 5e. Not exactly a representation of "Station", but I think it could certainly be adapted. Theirs is mostly to help solidify the fact that their many disparate cultures ... generally don't see eye-to-eye, but I could certainly see something for Al-Qadim where your Station with others is interpreted in a similar manner.
They use the levels of "Favored, Friendly, Neutral, Askance, Mistrust, and Unknown", which may allow for more dynamic reputations: Our 11th Level Beggar-Thief may be a veritable Prince of Thieves with the Favored Status with other such bandits and brigands, but certainly Mistrusted by the Mamluk who pursue him, and Unknown in The Pantheon Cities which he stays far away from.
Mechanically, if you wanted to incorporate this, you could make it where having these Reputations either adds a positive or negative to non-violent checks in an encounter with others: maybe +1d6 for Favored, +1d4 for Friendly, +0 for Neutral, -1d4 for Askance, and -1d6 for Mistrust. It's very easy to use Persuasion to convince your friends to let you stay longer than 3 days, but the Al-Badia who are askance of this party of Al-Hadhar would be a little harder to persuade.
This is off the top of my head, but it may allow a bit of Intrigue to develop, as well as player goals too: PCs may legitimately want to try and reach Favored with as many people as possible, which in turn leads to quests to help these people, etc., etc.