[Edit: By labor money I mean something slightly different from the labor tokens mentioned in the Gotha Critique. Labor money would be a form of money within commodity production and private property, whereas the labor tokens mentioned in Gotha are referring to a post-capitalist society in which commodity production (i.e. private property) has been abolished.]

The rest of the footnote makes it clearer, as well as other writing in Grundrisse and Poverty of Philosophy. The so-called utopian socialists wanted to keep commodity production while eliminating money, whereas Marx thought that money is necessarily produced by commodity production and can’t be done away with while keeping commodity production. So the connection between the Pope quote and labor money is simply that contemporary advocates for labor money wanted a situation in which all commodities could behave as money, which is what abolishing money effectively tries to do.

Full quote, bold added:

It is by no means self-evident that this character of direct and universal exchangeability is, so to speak, a polar one, and as intimately connected with its opposite pole, the absence of direct exchangeability, as the positive pole of the magnet is with its negative counterpart. It may therefore be imagined that all commodities can simultaneously have this character impressed upon them, just as it can be imagined that all Catholics can be popes together. It is, of course, highly desirable in the eyes of the petit bourgeois, for whom the production of commodities is the nec plus ultra of human freedom and individual independence, that the inconveniences resulting from this character of commodities not being directly exchangeable, should be removed. Proudhon’s socialism is a working out of this Philistine Utopia, a form of socialism which, as I have elsewhere shown, does not possess even the merit of originality. Long before his time, the task was attempted with much better success by Gray, Bray, and others. But, for all that, wisdom of this kind flourishes even now in certain circles under the name of “science.” Never has any school played more tricks with the word science, than that of Proudhon, for “wo Begriffe fehlen, Da stellt zur rechten Zeit ein Wort sich ein.” [“Where thoughts are absent, Words are brought in as convenient replacements,” Goethe’s Faust. See Proudhon’s Philosophy of Poverty]

The pope quote in Capital was probably borrowed from a section in Grundrisse ~10 years earlier, in a discussion on labor money

“Let the pope remain, but make everybody pope. Abolish money by making every commodity money and by equipping it with the specific attributes of money.”