Premise #:1
Although Stirner's philosophy is radically skeptical of moral judgements, it recognises the validity and communicabiliy of value judgements. The basis of Stirner's principles are an esteeming of the individual life governed by rational self-interest.
Premise #2:
Paradoxically, human self-interest is best fulfilled in self-giving, humility, and prioritising other's needs above one's own. This is not necessarily in conflict with the roots of Stirner's philosophy: if one recognises that they find maximal satisfaction in altruistic behaviour and follow it out of rather than being compelled to by delusions or "spooks", that may be perfectly resonant with amoral egoism. (Contrast with Ayn Rand's nonsensical moralistic egoism).
So far, the Catholic morality and Stirner's are not especially dissimilar, except for metaphysical disagreements.
However, here is where the two philosophies come into conflict:
Catholic ethics suggest that one should perform good deeds even when they experience no tangible uplift from it, when they derive no discernible satisfaction from it. It is legitimate to experience self-development, self-realisation and self-satisfaction through altruism, but it is illegitimate to negate others if one thinks they will find more satisfaction in selfishness, isolation and cruelty.
Christianity also assumes a base-level human essence where Stirner decrees there is none. Stirner considers the idea of an intrinsic commonality between men a limiting "spook", and instead considers the "creative nothing" the root principle/premise. Whereas Christianity says that humans have root causes and needs that can only be fulfilled by certain means, Stirner says that such a generalisation is ungrounded and false, and that such ideas may have no relevance to the individual, an entirely separate entity.
THEREFORE:
If the metaphysical bases of Christianity are in fact true, and its assertions about human nature do in fact apply to a universal principle to which all humans do (or can) correspond, then Stirner's value judgements must recede into the Christian system, since the egoist can only find full satisfaction and rational fulfillment of his self-interest in following the path outlined by the Christian ethic. The omnipotent, omniscient, omnibenevolent God wishes for the maximal fulfillment of all individual beings, and through submission to God all individuals will find their innermost being most fully, vibrantly and rewardingly expressed.