In the responsa collection of the Beth Yosef, Avqath Rokhel #32 he defends those who conduct themselves according to the Rambam, even in a place where the majority of people follow another poseq (in this case, the Rosh). The turn of phrase that indicates that one can do so regardless of their familial tradition is: "...especially if they have a tradition from their fathers..." In other words, a person should not be forbidden from following the Rambam ESPECIALLY if they have a family tradition of doing so, which implies that one should not be forbidden from doing so even if they don't.
However, there are other very important considerations to such an undertaking:
- To be a "Talmidh HaRambam" one must follow ALL of his leniencies and ALL of his stringencies: This is even stated by the Beth Yosef here in this teshuvah. This means only eating eating certain shekhittoth of meat (which cannot be found easily in Israel, and not at all outside of Israel), your wife wearing a hi-jab to cover her hair and neck, your young girls covering their hair as well, and this is only to name a few. The Jewish reality codified by the Rambam is a completely different reality in many respects to the one occupied by religious Jewry today. One cannot become a "Talmidh HaRambam" in order to eject from many of the stringencies of mainstream orthodoxy today and not follow the Rambam when he is strict or a da`ath yahidh.
- There never in history existed "Talmidhei HaRambam" as such: Throughout Jewish history since the publication of the Mishneh Torah there has never been a concept of only and always following the Rambam. Not in Yemen, not in Aleppo, not in Eress Yisra'el, nowhere. There were always minor exceptions in both matters of minhagh and halakhah as there most likely was even among those whom the Beth Yosef defends in his teshuvah. Even the Rambam himself and his son, Rabbenu Avraham, did not follow the rulings codified in the Mishneh Torah 100%. There are various reasons for this, not the least of which are situations of halakhic need which require certain innovations or the invocation of other opinions. To be a "Talmidh HaRambam" in the sense of following the Rambam in absolutely every opinion he holds - to the exclusion of all else - is a relatively new phenomenon that is not at all possible and has caused many problems among those who have tried.
- One needs a competent Rav in the tradition of the Rambam: The best way, le-`aniyuth da'ati to follow the Rambam in our time - and in any time - is to connect oneself with a Rav in the tradition of the Rambam. This would mean either a Yemenite, a Syrian, or many of the Sefardic rabbanim in the world today. Or, one could also find a meqori Rav to learn from who is largely based on the Rambam (but not exclusively so), such as Rav Dawidh Bar Hayyim of Yerushalayim. The fact is that Rav Qaro in the Shulhan Arukh rules like the Rambam through direct quotations approximately 85% of the time, so Sefaradim who are true to the Gemara over the Qabbalah are fairly close to the Rambam most of the time. Not only will this help to avert the plethora of errors made by those who try to forge their own path in the Rambam (often without even being able to read and understand Hebrew), but it will also help a person be consistent and able to navigate all of the non-ideal halakhic situations that arise in the course of normal everyday life.
As far as how such people are treated in halakhah, they are treated like every other religious Jew. However, in today's haredi world, anyone who does anything different than the status quo is often branded an "apikoros" for daring defy the words of the [Ashkenazi] "gedolim." If Sefaradim are often treated like second-class citizens, I can tell you that Yemenites are treated even worse than that many times for the "crime" of following the Mishneh Torah over the Shulhan Arukh. Many reading this may not like such a statement, but I maintain that my assessment is true and accurate. So, I am not saying that one should not pursue such a path, but only that one should know what they are getting into before they do so.
Hope that this helps.