The Radvaz (Teshuva 522) writes that the concept of אין מעבירין על המצות is only d'rabonon and that the drasha of ושמרתם את המצות is only an אסמכת. According to this approach the requirement to do the דישון מזבח הפנימי prior to the הטבת הנרות is only m'drabonon, but m'doraysa there is no particular order. The Radvaz proves this from the approach of Rabbeinu Tam (cited in tosafos) that one must be careful to put their tefillin in the bag in a way where they will not be forced to pass by the tefillin shel rosh to get to the tefillin shel yad. The implication is that if their shel rosh was on top, they would indeed pass their shel rosh, violating אין מעבירין על המצות to put on their shel yad first (to maintain the order of the pasuk). The Radvaz explains that if אין מעבירין על המצות would be d'oraysa, why would we violated the issur of passing by the shel rosh, just to fulfill the mitzvah of putting on the shel yad first. Therefore, he concludes that the entire concept must only be d'rabonon, so the order of the pasuk which is d'oraysa trumps the issue of אין מעבירין על המצות.
The Maharatz Chiyus challenges the Radvaz based on Rashi in Succah 25b who implies that the concept of אין מעבירין על המצות is indeed d'oraysa. It seems to me that Rashi here also implies that it is d'oraysa. When the gemara discusses how to use the extra terms בבקר written by the שני גזירי עצים, and rejects an alternate approach because we would have nothing left to use to divide the neiros which the pasuk seems to require. Rashi comments that we could use the דישון מזבח to divide the neiros, 5 before and 2 after. Rashi says this is not possible because that would demand passing the מזבח to get to he menorah and would violate אין מעבירין על המצות. In this context rashi is using אין מעבירין על המצות as a premise to explain the pesukim, clearly implying that it is a torah recognized concept, thereby rendering it d'oraysa.
However, it seems to me that the Tosafos Yeshanim understands that it is only d'rabonon. Tosafos Yeshanim ask why do we need to say that the wood on the ma'aracha of the outer mizbeiach (שני גזירי עצים) proceeds the דישון מזבח הפנימי because of the burning wood is hechsher mitzvah, it can simply be because of אין מעבירין על המצות and one reaches the outer mizbeiach first. Tosafos Yeshanim answers that there would be an alternate logic that things done inside the heichal are more important - מצות פנים עדיפא, which would have overridden אין מעבירין על המצות, so we need the sevara of מכשיר עדיף. If the logic of מצות פנים can override the issur of אין מעבירין על המצות, it must be that he is understanding that אין מעבירין על המצות is only d'rabonon because if it were d'oraysa, how can a sevara override it! This would support the Radvaz.