I can even provide examples. From Dragon Age Inquisition we have Cassandra, whose story arc centres around her belief in the organisation she's a part of. She remains Righteous throughout but her big conflict is in reconciling the ideals she swore herself to with the fact of the corruption within the order she's part of, and deciding if organisation is even worth trying to salvage. She remains true to her ideals in the end but she still has to grapple with the morality of the system she's been a part of.
Excellent example using one of my favourite game characters. She remains loyal to her religion while recognising that the church needs reform (in DA:I).