In his Mishna Commentary to Sanhedrin 10:1 Maimonides lists as his 5th principle the prohibition to pray to an angel even as an intermediary. He counts this in his enumeration of his 13 principles in his Mishne Torah as well (Hil. Tshuva ch. 3).
How then are we to understand his codification in Laws of Tfilla (7:5) of a prayer addressed to angels
וְכָל זְמַן שֶׁיִּכָּנֵס לְבֵית הַכִּסֵּא אוֹמֵר קֹדֶם שֶׁיִּכָּנֵס הִתְכַּבְּדוּ מְכֻבָּדִים קְדוֹשִׁים מְשָׁרְתֵי עֶלְיוֹן עִזְרוּנִי עִזְרוּנִי שִׁמְרוּנִי שִׁמְרוּנִי הַמְתִּינוּ לִי עַד שֶׁאֶכָּנֵס וְאֵצֵא שֶׁזֶּה דַּרְכָּן שֶׁל בְּנֵי אָדָם. (Other versions of the text include even more prayer).
This formulation is more difficult as he writes elsewhere that the angels that accompany man are his positive and negative inclinations. “It is to the good and the evil inclinations that they refer in their well-known words," Every person is accompanied by two angels, one being on his right side, one on his left." In the Babylonian Gemara (Shabbath 119b), they say distinctly of the two angels that one is good and one bad.” (Moreh Nevuchim 3:22; Friedlander Trans.)
For a similar presentation of the angels that accompany a person, see Hil. Mezuzah 6:13.
Is it permissible to pray to one's inclinations?
There is indeed at least unnamed but very early Rabbi who believed this prayer to be proof that there's no prohibition of praying to angels. See the responsum published by Simcha Emanuel in Hamayaan, Tishrei 5758. (This article attributes the same responsum to R. Eliezer Rokeach, though this is not necessarily correct).
Also, before answering the question directly, I'll note that Maimonides/Rambam does not believe that Biblical or Talmudic angels are to always be understood as man's inclinations (see the Commentary to Sanhedrin 10:1, for example, where they are intermediaries for prophecy). Just because he offers that explanation of a passage in Shabbos 119b, he wouldn't necessarily believe the same about these "angels".
Actually, there's a huge body of literature regarding what exactly would be problematic, in Maimonides'/Rambam's view, regarding 'praying to' (or making requests of) angels. I can't find a link right now to all of the many (approx. 30) sources that I know of myself. However, there are less sources dealing directly with this particular prayer, and I'll be happy to discuss those answer.
One explanation is that Maimonides/Rambam probably did not have the version of the text that you cite above, but rather a version that lacked the phrase "עזרוני עזרוני" (as testified by the Bodleian MS. Huntington 80, the copy autographed by its great author). Thus, the only problematic two words (which seem like a 'prayer'), would be "שמרוני שמרוני", "protect me". However, R. Yehudah ben Yakar, in his commentary to the Siddur, explains that the phrase should be translated as "wait for me", just as the verse, "ואביו שמר את הדבר". (He recognizes that this renders the next phrase, המתינו לי as redundant, and his response to that issue is merely to not include it). This explanation is also suggested by R. Meir HaMeili of Narbonne (in the book Milchemes Mitzvah, printed in the back of his Sefer HaMeoros on Maseches Berachos)
Rabbeinu Manoach, a very early commentator on the Rambam, writes that this prayer is indeed directed not to angels, but to certain intellectual faculties. By saying this 'prayer' before entering the lavatory, a person is actually reinforcing (to himself) that he shouldn't be fully using his rational faculty while in there (I assume because one is not permitted to study Torah in the bathroom) but at the same time doesn't want to abandon it completely.
Another source that I know of which addresses this issue directly is R. Yaakov Emden in his commentary on the Tur, Mor U-Ketziah (O.C. 3). There, he explains that because he refers to the angels as משרתי עליון, it's clear that he doesn't believe that the angels have any independent agency, but he's speaking to them as emissaries of God. He believes that doing so avoids running afoul of Maimonides' 5th principle, which is merely that is isn't worth requesting anything of angels because they cannot act against God's will; here, a person is merely asking that they perform God's will happily. (See Abarbanel in Rosh Amanah ch. 12, and R. Moshe Feinstein, Iggros Moshe vol 8, O.C. 5:43:6). Personally, I'm not so convinced that Rambam/Maimonides would really be OK with this, especially if his source is the Talmud Yerushalmi 9:1)
R. Asher Weiss discussed this question in a shiur from September 2006 (available here) and said that careful reading of Maimonides in both his Commentary to Sanhedrin as well as in Hil. Teshuvah 3:7 shows that he only prohibits prayer to angels if done as an expression of their status as intermediaries between oneself and God or serves them. However, if one merely "prays" to them to ask them a favor, this is not considered serving the angels in any way and is thus permitted. (However, this still seems to be against the Ramban in his "Toras H' Temimah", R. Yehudah ben Yakar in his commentary to Tachanun, and R. Shimon ben Tzemach Duran in Magen Avos ch. 4)
