What if the person believes in in some greater good for altruistic reasons, but thinks that achieving that good requires harming others?...
Absolutes rarely capture the complexities of the real world, of different belief systems etc...
In 1983 I abandoned alignment as written, and replaced it with a relative system. Whenever alignment had a rule impact, I asked why. Usually, it was because a divine effect. In those instances, I asked whether the divine being that granted the power would consider something to be good or evil. Two clerics casting detect evil in the same situation might get different results. It worked really well.
As the editions lessened the impact of alignment, I dropped it entirely. When I told players I didn't use it, it almost always created concern, discussion and some degree of consternation. If I just didn't reference it, there was really no notice of it not being used.
When 5E came out, I started to have people state an alignment for their PCs again. However, it is just one of a score of things I ask them about. Flaws, traits, bonds, ideals, (back) stories, family, friends, goals, fears, etc... It is there to help them build their PCs and create a concept. It is just a starting point, but if a player said , "Chaotic Good" and then started to play "Neutral Evil" (IMHO), I would not bring it up, bat an eye, or care.
With these approaches, otuside of theoretical arguments, alignment has not been a problem for me in a looooooooooooooooooooooooooonh time.