Battlestar Galactica: what is the most critical resource?
As with most games, it depends. It would most likely shift some using the variant rule as well, but it isn't clear to me exactly which way. You lose the game if any resource hits 0, but depending upon different game states, different resources may be more important than others. For example, if you are already at 8 distance, you can probably safely allow Fuel to be reduced to 1 rather than Morale which comes up more often on the Crisis cards. If your President is a cylon on the other hand, they most likely won't be giving Inspirational Speeches to improve your morale (even worse, if your Admiral is a cylon too). Which characters are being played in the game, and which (if any) are cylons probably has the biggest effect on the importance of individual resources.
Here is an analysis that someone wrote up on BGG.  The major points are:

Fuel: You start with 8, and you need to travel 8. There are 21 destination cards, and most Destination cards allow you to move one, at the cost of one fuel. You need to save/gain fuel at some point. One third of the cards allow you to move 2, but only cost 1 fuel. Of the 70 Crisis cards, 10 can cost you fuel, but in half of those the Admiral is given a choice of losing other resources instead. If the Admiral isn't a cylon, it is unlikely you will run out of fuel.
Food: You start with 8. Food is a volatile resource. Food Shortage shows up 9 times in the crisis deck, and the President has the option of throwing away cards or losing food. On 6 other skill check cards, if you fail to pass you lose food, these vary in color. Food is one of the few resources where it is possible to lose two steps in a single turn. If the President isn't a cylon, it is unlikely you will run out of food.
Morale: You start with 10. Morale is very skill check dependent, and in 19 of the 70 cards it is possible to lose morale. Most checks are Green and Yellow. Most of the skill check are pretty easy to pass. In 9 of the cards, the Admiral has a choice of losing Morale or other resources. The president can give Inspirational Speeches to raise morale (4 of 17 Quorum cards). Horde Yellow and Green cards to avoid losing Morale, and pray your Admiral isn't a cylon.
Population You start with 12. Most civilian ships have 1 population. 12 Skill checks have the potential of losing population, but 4 of those give you a choice, leaving only 8 must pass skill checks. The checks are usually very hard to pass, and usually require tactics. If you defend your civilian ships, you can use the FTL early, and lose 5 skill checks, and still not lose due to 0 population. If you don't lose civilian ships to cylon attacks, you can jump early and avoid more Crisis cards.

You also might want to check out a rather detailed distribution of the cards in Battlestar Galactica.