The question could just as easily be:
Should a person die for their political BELIEFS?
Should a person die for their personal BELIEFS?
To me, the more important questions are:
1) Does the person genuinely believe whatever it is from informed choice, or are they being coerced?
For example, many people have been forced, often for political or religious ideologies, to kill themselves or be killed. Kamikaze pilots, suicide bombers, etc.
2) Is the potential for them to die coincidental, or an intentional or required part of that belief?
Again, if the prospect of death is a deliberate and intentional part of the 'belief' (whatever it is), then that's usually not a good reason. Again, the above example of kamikaze pilots and suicide bombers come to mind.
However, if the prospect of death is coincidental - in other words, it's not inherently necessary, but happens because of, say, the action of enemies, or even simply bad luck - and the decision to face death is chosen consciously by the individual, then I don't see that it is necessarily wrong.
The third question would be What exactly is it you are prepared to die for?
People are prepared to die for all sorts of things - soldiers for their country, police and firefighters to protect others, political activists for their cause, even extreme sports people for their favourite activities - not all of them would be considered healthy or meaningful reasons to put your life on the line.
Then there's the question of whether risking your own life would endanger other people's lives? Or do you have dependents who would be harmed by you sacrificing your life?
TL;DR - I think it depends on a whole lot of other variables than simply "should you"/"shouldn't you".
I agree with BluesBrother's general point that in an ideal world, no-one should have to choose between their beliefs (religious or otherwise) and their life, but sadly, things are not always like that.