That will only work if the person has no emotional attachments to his current beliefs.

That's why it's important to acknowledge that the idea they are using is useful in some situations, just not in others. It's a way to "leave them a path of retreat", a way for them to take a step back and not totally "lose" a belief they found useful and effective (and that they have an attachment to), but to realize that it's just not useful in all situations.

No. People might accept cultural relativism because all their friends think that cultural relativism is cool.

In that one sentence, you are both dramatically overestimating and dramatically underestimating the vast majority of people at the same time.

Overestimating, because most people don't discuss with their friends the virtues of cultural relativism on a regular basis. And underestimating, because the people that do generally are more thoughtful, philosophical types, who tend to hold their beliefs for actual reason.

Keep in mind that "cultural relativism" isn't anywhere close to the lowest common denominator here. It's several steps more rational then the lowest common denominator, which is "my culture (Christian/American/white/English speaking) is the best culture, and anyone who disagrees with it is either an idiot, evil, or both".

Cultural relativism is a somewhat more rational level reached by people with a certain amount of education and intelligence, or who come from a more cosmopolitan/open minded background. It's not the most rational level, certainly not if they try to apply it to sciences or if they use mangled versions of it to defend bizzare belief systems, but it's not the least rational level either; we're talking about people who are generally already in the top 20% or so. And people who are cultural relativists tend, almost by definition, to be willing to listen to other points of view; they're more likely to hear you out, if you appeal to them on a rational level and don't treat them like idiots (which is sounds like you're doing right now).

If you want to convince the kind of person who is religious because he believes the promise that being religious leads to a happy life, than you have to play on that level.

But we're not talking about narrow minded conservative religious types; they, almost by definition, hate the idea of cultural relativism (because their culture is the only one that's right). We're talking about people who have moved past that.

Anyway, people who are religious are VERY resistant to hearing recognizable religious-style arguments being used for what they deem to be anti-religious purposes. They have a lot of resistance to the meme, because they carry a version of it themselves. It's a reason that devout Christians don't, as a rule, become Scientologists; they're already protected against that type of mematic attack. It's also why very religious Christians are so likely to call ideas like the singularity or transhumansim a "cult" and thus reject it; if you're using something that looks to them like a religious argument to "convert" them to a "different religion", their meme immune system rejects it instantly. (Obviously ideas about transhumanism and the singularity are not actually religions, but that doesn't matter.)