My reply, before reading other replies, is that the question is wrongly posed. The described phenomena can be part of a causal universe, because they are causal processes.

Consider the psychic cousin. I draw a card from his deck - it is (say) the three of clubs. Let us further assume that he correctly guesses the card that I have drawn, and does so in 99% of trials. In such circumstances, his statement of the card that I have drawn ('you have drawn the three of clubs!') is caused by my drawing the three of clubs. The mechanism of that causality may not be known, but it is there.

Similarly for the example of "communing on a deep level with the entire universe in order to realize that your partner truly loves you" - there's a causal link, there, and the cause is "your partner truly loves you". (Personally, I'd prefer to check the conclusion by some other means in order to prevent observer bias effects, but this becomes tricky for this example).

Purely spiritual phenomena, therefore, are firmly inside the realm of causal processes, even if they are not yet fully understood.