Rephikul, did you consider figuring psychology of a person into that? More importantly, the 'groundless beliefs,' that your so adamant against?
While they might be 'groundless' they are still important to figure in. Survival is a complex calculation of things, though much of it can be summed up as cost and benefit as many have pointed out. All foods impart a certain level of benefit (calories, vitamins, minerals, etc) they also impose a cost (Energy spent to obtain the food). If the given food is in violation of beliefs, it increases the cost. Not just from a values stand point, but also from a physiological stand-point, as being forced to violate beliefs will cause stress. High levels of stress can cause health problems, which could potentially lead to death.
Now you might say say that the stress-induced death from this is cause by 'groundless beliefs' but contemplate this: Why do people follow those beliefs? Generally there is a reason, and the reasons are extremely varied. Some, like most western religions, are followed to attempt to reach paradise in the afterlife, something science can neither confirm nor deny. Other beliefs though are typically followed so the person feels better about themselves. This in itself is a benefit, as feeling better about oneself can help reduce stress and other negative emotions. Enough 'good feeling' can promote better health, and better thinking. So while the sustainence options are artificially limited, in theory at least, the person will be more able and more active to utilize the 'available' food sources.