In D&D 5e, the last part of the Sentinel feat contains this text:
When a creature within 5 feet of you makes an attack against a target other than you (and that target doesn’t have this feat), you can use your reaction to make a melee weapon attack against the attacking creature
Thematically, why shouldn’t you get the opportunity attack if the target has Sentinel? I can’t think of any flavor/narrative reasons why your ally having an ability would prevent you from using your own ability.
If that clause was included strictly to prohibit combos among fellow sentinels, is there an official source that says as much?