From the Schengen Borders Code:
Entry conditions for third-country nationals
- For intended stays on the territory of the Member States of a duration of no more than 90 days in any 180-day period, which entails considering the 180-day period preceding each day of stay, the entry conditions for third-country nationals shall be the following:
(a) they are in possession of a valid travel document entitling the holder to cross the border satisfying the following criteria:
(i) its validity shall extend at least three months after the intended date of departure from the territory of the Member States. In a justified case of emergency, this obligation may be waived;
(ii) it shall have been issued within the previous 10 years;
(b) they are in possession of a valid visa, if required pursuant to Council Regulation (EC) No 539/2001 (25), except where they hold a valid residence permit or a valid long-stay visa;
There's nothing about the passport and the residence permit having to mention the same nationality.
If a traveler appears with a residence permit listing a nationality different from that of the passport, the border guard could suspect that the passport and the residence card do not belong to the same person. But the other biographical and biometric data should make it clear that the documents do in fact belong to the same person, and if that person is the traveler presenting them, then the traveler will have met the entry condition cited above.