So, TECHNICALLY. When somebody chooses to be a Missing Nin, they become Neutral? That way both good and bad will be after them..Right? If they are bad, other "bad" ANBU wont want to kill them, they would want to unite and become an even stronger evil "force" So they would HAVE to be neutral..no?
Not quite.
The best way to put it, is there alignment wouldn't mean a thing. When choosing missing nin, a person is only for themselves, not evil, not good, and not neutral. Outside of chaotic neutral, most neutral people have a sense of what is right and wrong. A missing nin is for themselves(but they can still have personal values) and their own goals and desires very much like Tsunade(good)before being the Hokage going from casino to casino piling up debts, Jiraiya(good) not forgiving himself for not stopping his friend Orochimaru, Sasuke(neutral) just seeking more strength to defeat Itachi, and Orochimaru(evil) wanting to learn every jutsu in the world including forbidden one's. If there was an alignment called 'Egocentric' that would fit the mold.
Contrary to what you think, evil doesn't always want to team up with evil. If that was the case Orochimaru would have stayed with the Akatsuki, and they wouldn't have been after Orochimaru at all. All of the Seven Swordsmen of the Mist would be together instead of separated doing their own desired tasks. Evil doesn't always want company especially when they consider one competition or when there is profit to be gained by eliminating a competitor(rather good or evil) .
Simply put if you decide to be a missing nin, KNOW FOR A FACT THAT YOU WILL BE ATTACKED BY BOTH ANBUS' IN THEIR RESPECTIVE VILLAGES. One doesn't have to choose to be a missing nin and get a possible heads up on an rasengan item, but if one does decide to be one, it won't be easy. No village will be safe (outside of the one that people pay a hefty price to enter and Konoha). It's a part of the trade off, if one wants the possible rasengan item and one wants to keep their hard earned stats, castles, gems, and etc... then they can, but there has to be reciprocation.