Although Islam is considered monotheistic I would imagine that in a case of 'oness' (coercion) one would still not be allowed to convert. Is conversion to Islam considered to be a case of יהרג ואל יעבור (One should choose death over transgression.)? Why?
The Rambam in his אגרת השמד says outward acceptance of Islam is not ייהרג ואל יעבור. On the other hand, the Radvaz quotes the Ritva as saying that this is ייהרג ואל יעבור. According to the Rambam, outward acceptance of Islam is not ייהרג ואל יעבור because Islam is not עבודה זרה, and even though it is heretical because it denies the Torah, one does not have to give up his life for claiming to believe in Muhammad. The Ritva on the other hand would hold that since accepting Islam means rejecting the Torah for Muhammad, it is ייהרג ואל יעבור.
(For some secondary sources on this topic see Haym Soloveitchik, "Maimonides' Iggeret ha-Shemad: Law and Rhetoric"; Marc Shapiro, "Islam and the Halakhah.")
I recently went to a shiur on this topic after posting this question. The Rabbi said that there is much debate on what the Rambam actually held with regards to this i.e. whether he was writing as a response to the Jews of Fez and their 'coerced conversion' at the hands of the Almohads. The Rambam was writing in response to an unnamed chacham who was espousing very harsh claims that these Jews were 'goyim' and would do better not to daven and perform any rituals at all. The Rambam went to Fez, Morocco, (for unknown reasons) in the thick of Almohad control without being subject to the harsh sanctions. His letter (iggeret hashmad) was in response to this chacham.
The Rambam made a few major points to this specific community in Fez:
1) Judaism is not all or nothing. Every mitzvah is important regardless of your status. The mitzvah of a tzaddik is important and so to is the sin or a rasha. Nothing is beyond any of us.
2) Although they had declared the 'shahada' (basic statement of Islamic conversion that Allah is G-d and mohammed the prophet) they clearly did not mean it and the Almohads knew this. The Rambam was reassuring the community to continue practicing Judaism and to not feel the overwhelming guilt that this chacham was placing upon them. [As wfb mentioned above, others disagreed with the conversion and said that it would have been better to have died, because declaring belief in mohammed would be contrary to (at least) the Rambam's 13 ikarim, namely that Moshe's prophecy being infallible.]
3) One cannot slander an entire community.
4) Although the conversion is not ideal, they should at least yearn and try to escape if the time was right and not a danger to their life. Otherwise they could lead astray and fall into a false sense of security.
Although the iggeret ha'shmad seems to sway towards the conversion not being ייהרג ואל יעבור there are those that debate this. The Rambam doesn't pasken lechatchila what to do in this situation, its a response to a situation; which of course gives rise to this debate in the first place. Some say that within the Mishneh Torah itself it contradicts the Rambam's overtones in this very letter. (see Chaim Soloveitchik as mentioned above)