In America, maybe, but not necessarily in other countries.  I'm not even sure its an official policy in some countries, which is why I think some people still slide under the wire and get burnt later like the man in the initial article.  I became super curious and looked this up today, even messaging my friend to get the details.  Pardon me for not using correct military terms (I'm not military.)

1) It appears that in Canada they are excluding more and more people with allergies from joining the military.  Some people still seem to get through though, whether it be because of their particular allergy not being common, the position they apply for, or random chance I don't know.  Back when I went through recruitment it wasn't considered as much as it is now.

2) My friend fully disclosed his egg allergy up front (back at the same year I went through recruitment) and was accepted and posted on foreign soil twice (Germany, Afghanistan).  He often went hungry in Afghanistan because he could only eat in the crew mess.  He would hoard and trade food whilst in Afghanistan.  Probably not ideal and he doesn't recommend it; he would leave on medical grounds if he were posted to a front line location again.  (Germany was fine.)

3) There are some people in the military that develop food allergies as an adult (think shellfish) and keep their positions.  I'm not sure if they are weeded out through annual physicals or what.  My friend knows several others who carry EpiPens - for stings, for shellfish, and for a preservative in their MRE meals.  They have an orange tab on their uniform to identify them.  (I'm not sure if that is official or not, but that's what he told me.)

After conversing with my friend, it certainly seems like FAs should be a universal disqualifier.

It surprises me he got as far as he did in the first place.

Haven't FA's always been something that disqualifies you from service?  I do know that after receiving some info from a military college, I looked up the medical info and also found eczema could disqualify you too. 

I have grown up in military towns.  People with food allergies are allowed to join the military here (and are subtly identified on their uniforms as having EpiPens) but I am not sure how it works with various postings and at sea. The larger ships and bases have full medical centres, like small emergency rooms, and can treat and stabilize some pretty serious stuff.  I have to wonder if this was a case of misinformation and poor planning at several levels.  Someone with a life-threatening medical condition shouldn't have been placed in such a vulnerable posting in the first place.  Though, that brings up more questions of surely this person isn't the first one to have food allergies or a reaction at sea, how could his medical be completely revoked, and more... The military is often backwards with its logic though... So you never really know.  Unfortunate story no less.

I, too, dreamt of a military career but was squashed at the medical phase (for a condition they deemed too risky for the position I applied for) before I ever got to training.  My food allergies weren't the reason why, either. 

ETA: I know Canadian Armed Forces will send people with FAs to overseas postings.  I know one person with FAs who had a posting in Afghanistan... I'm not sure what position he had though or if he was ever out on assignment where they rely on MREs.  (He couldn't eat the MREs.)

It kind of makes sense. He was lucky that a helicopter medevac was available and that he was in range of a port. What would have happened if he was thousands of miles away at sea?

The US Army/Navy sent me tons of mail and recruiting calls as a teenager. The moment I told them I had food allergies I was removed from all further mailing/calls. They don't want someone who can die from inadvertent exposure to an allergen to be far away from proper medical attention.