Well, I think the vast majority of Burmese are avid meat eaters and are probably the most devout Buddhists I have ever met (that is, those that I met).
Don't conflate the eating of meat with killing - they're not the same.
If you wish to adopt a vegetarian or vegan diet as an expression of compassion arising from your practice, that is excellent. But it is no better nor worse from a kammic point of view than a diet that is not vegetarian nor vegan.
Who kills the animals in Myanmar? Probably not Buddhists. Killing is very bad kamma and a violation of the 1st precept. Burma is not entirely Buddhist- there are 4% of Muslims and of Christians and 1% of Hindus (the Hindus probably wouldn't kill either). Those religious groups would probably do the killing. In TIbet, non-Buddhists are usually the ones who kill the animals there. If the world was entirely composed of devout Buddhists, there will be no meat eating (except animals that have died of natural causes- this is somewhat less objectionable). The rules for bhikkhus were meant so that the bhikkhus would not offend lay followers by rejecting food. It is an outdated social rule. Buying meat is akin to "encouraging killing." One is indirectly encouraging people to kill so that you can have more meat. I oppose the notion that "I didn't kill myself, so I don't get any kammic demerit"- One is, by their actions, supporting killing of sentient beings.
I have nothing personally against meat eaters. Even vegans contribute to the killing of insects and other tiny creatures. One cannot be perfect. But one should at least try to reduce dukkha for other beings. Where is compassion? These beings suffer, just like we do. What if you were the animal, which you very well could be in you next birth, how would you feel? For Bhikkhus and Bhikkhunis, there is no choice. We have a choice! We can reduce other's suffering. I highly doubt the Buddha ate meat (don't give a reference, I won't believe it). He was so kind to animals (against sacrifice and the swan story).