I read that the Rambam considered a Jew who converts to Islam NOT to be an Apikorus(אפיקורוס)\heretic or an ovdei avodah zarah, as opposed to a convert to Christianity who he considered to be heretic and avodah zarah. Is this true? According to the Rambam and other rabbis, is it permitted for a Jew to convert to Islam?
In his Igerret Hashmad he teaches that Jews forcibly converted to Islam are not automatically or necessarily heretics. However he also limits this to the case presented to him and says that even in that situation martyrdom or fleeing is an option. http://thejewishchronicles.com/maimonides-iggeret-ha-shemad/ http://www.oxfordchabad.org/templates/blog/post_cdo/AID/708481/PostID/13360
There is a Sefer HaNehHomoh by the RaMbaM's father, Rabbi Maimon HaDayan HaSafardi (http://www.hebrewbooks.org/26889) He writes a whole letter to the jews who were forced to convert to islam in his time period. He quotes and explains posukim in order to calm them down and to tell them that they can still perform misSwoth and are still jews. The community at the time were fluent in arabic and not so educated with regards to judaism or its language, due to persecution and what have you. Therefore Rabbi Maimon translated for them the prayer of havineinu, which is a shortened version of the standard shamonei asrei prayer, into arabic, for the people didn't have time to pray or learn. He also says that there will come a time when the oppressors will stop oppressing us and we can live a normal jewish life. From this we see that it is not ok to convert to islam because if it was ok, jews would have been converting long ago without oppression. Not only that RaMbaM calls muslims apikorsim for saying that the Torah was changed. Your statement above is wrong. The christians are ovdei avodoh zoroh, but not apikorsim, muslims are apikorsim but not ovdei avodoh zoroh.
While you are correct that Islam is not heresy, that alone is not sufficient reason for a Jew to convert.
There are many things which are not accepted by Judaism but are not considered so damaging as to be branded heresy. For example, if I say I believe my rabbi is a prophet - that is a statement Judaism will roundly reject according to the mainstream opinion on what constitutes a prophet. But since there is nothing in the fundamentals of Judaism that says my rabbi is not a prophet, my belief is simply a rejected notion but not heresy. Similarly, if I believe that roses are blue and violets are red, I am not a heretic, but of course I am still mistaken.
The same Maimonides who said in his Iggeres HaShmad that one who converts to Islam is not a heretic, denied, in the same letter, that Muhammad was a prophet. He would also certainly deny, therefore, that the Quran is a revealed text. So while according to mainstream Jewish opinion Islam doesn't violate any of the fundamentals of Judaism which would render it heresy, it is still a mistaken belief system.