There may be some subtle differences in how alcohol is metabolized when your hormone levels are at low points, but physiologically, there is no explanation that can be measured quantitatively.

More likely, there is a well researched phenomenon that your psychological state has much to do with how quickly you feel effects of ETOH in your body, and many women are more "down" and vulnerable emotionally during their menses, and ETOH will cause impairment more quickly and alter mental status.

Getting "drunk" should always be avoided for obvious reasons so what your body is telling you is to moderate, no matter what time of cycle it is.