Mongolia is the world's least densely populated country. I can't imagine how they would have effective propaganda anywhere outside Ulaanbaatar, or how they would've done any sort of rationing to their nomadic population. Were there any attempts to ration to the nomadic peoples and suppress their shamanistic religions? How effective were these attempts?
I don't fully get what you mean by "rationing". In any case, widespread rationing didn't occur until after communism fell (see "картын бараа"), and even then mostly in Ulaanbaatar. The countryside remained essentially self-sufficient, the Mongolian diet is basically meat. As an aside, I'll mention this is why hunger has never been a major issue, even with widespread poverty, Mongolians subsist on meat and dairy alone, foodstuffs raised on the pasture by herders.
As for religion, it was highly suppressed, at the eve of communist rule, almost half of the male population were lamas, syphilis had gripped the entire region, and it was said that the Mongols were a dying breed (see Cyril Edwin Black; Louis Dupree; Elizabeth Endicott-West; Eden Naby (1991). The Modernization of Inner Asia. M.E. Sharpe. pp. 116–). The great purges that occurred during the 1930s essentially wiped out the Buddhist clergy, with only one monastery left functioning (Gandantegchinlen in Ulaanbaatar), but even then it was more for show (for US VP Henry Wallace's visit in 1944, in fact). Even now, half of the population identify as atheist/irreligious.