All above me are very good, and I agree that listening to your intuition is important. The High Priestess is also about intuition, but I feel it's more like the application of it and active practice of this mindfulness, as well as the pursuit of more. There's a sense of certainty with the High Priestess that isn't there with the Moon. The Moon is more of a mysterious sense that doesn't come from one's self, but out of the blue and can be confusing or dreamlike. Perhaps the Moon intends to tell X to be cautious, not because of what X already knows or suspects about Y, but rather because of the things that X can sense but not necessarily understand. There may be an underlying feeling without an obvious cause and confusion because of this, and depending on the context, X might want to look into communicating this with Y, or looking to see if it can be cleared up some other way.
Another interpretation that is suddenly banging against my head is hero worship. As others have said, X should avoid becoming swept away by the way Y presents themself, and avoid idealizing or exaggerating Y's qualities, whether good or bad. Often what one sees isn't the whole picture, and the face we show others never is.
And yet one more that just came to mind is to do with the phases of the Moon. The moon's phases and positions in the sky change, but they are always predictable with those who know how to do so. Maybe this encourages X to remember the past patterns of Y and understand that they will repeat themselves eventually if it hasn't happened already. X should really look and see if what Y is doing now is simply something X has seen before in a different form. Change happens and always seems new, but history also repeats itself. It's important to compare the past to the present, and think about whether new things are just old things you've forgotten.