"You don't use your mind to think about religion." - J. R. "Bob" Dobbs, Church of the SubGenius.
The question you asked is how to convince your friend not to become a Catholic. That's the question I'll answer, but it's the wrong question for you to ask.
The Episcopalian faith has much of the content and structure of the Catholic faith, but it is (I hear) more accommodating to women and to non-straight people. Perhaps this might be a better fit for your friend.
The blogger behind ravingatheist.com became a Christian. To his or her credit, the blog remains as it was and the entire record of his or her conversion is there for all to read. This might serve as a guide to you and to your friend, not necessarily in the direction either of you want to go.
If no good can come of or be retained after your friend's conversion, then go ahead and try emotional blackmail. Say 'if you do this I'm not talking to you any more.' If that doesn't feel comfortable, you are starting to ask a better question than how to stop your friend from converting.
If no good can come of or be retained after your friend's conversion, then go ahead and try emotional blackmail.
Please don't. Becoming a Christian is not the end of the world. People are remarkably good at compartmentalizing, and a large part of the reason he's likely thinking of converting is probably that there's a large, supportive community waiting for him if he does. Demonstrate that he has a community if he doesn't convert, don't threaten to take away his current one. But emotional blackmail is not the way to go.
I recently learned that a friend of mine, and a long-time atheist (and atheist blogger), is planning to convert to Catholicism. It seems the impetus for her conversion was increasing frustration that she had no good naturalistic account for objective morality in the form of virtue ethics; that upon reflection, she decided she felt like morality "loved" her; that this feeling implied God; and that she had sufficient "if God, then Catholicism" priors to point toward Catholicism, even though she's bisexual (!) and purports to still feel uncertain about the Church's views on sexuality. (Side note: all of this information is material she's blogged about herself, so it's not as if I'm sharing personal details she would prefer to be kept private.)
First, I want to state the rationality lesson I learned from this episode: atheists who spend a great deal of their time analyzing and even critiquing the views of a particular religion are at-risk atheists. Eliezer's spoken about this sort of issue before ("Someone who spends all day thinking about whether the Trinity does or does not exist, rather than Allah or Thor or the Flying Spaghetti Monster, is more than halfway to Christianity."), but I guess it took a personal experience to really drive the point home. When I first read my friend's post, I had a major "I notice that I am confused" moment, because it just seemed so implausible that someone who understood actual atheist arguments (as opposed to dead little sister Hollywood Atheism) could convert to religion, and Catholicism of all things. I seriously considered (and investigated) the possibility that her post was some kind of prank or experiment or otherwise not sincere, or that her account had been hijacked by a very good impersonator (both of these seem quite unlikely at this point).
But then I remembered how I had been frustrated in the past by her tolerance for what seemed like rank religious bigotry and how often I thought she was taking seriously theological positions that seemed about as likely as the 9/11 attacks being genuinely inspired and ordained by Allah. I remembered how I thought she had a confused conception of meta-ethics and that she often seemed skeptical of reductionism, which in retrospect should have been a major red flag for purported atheists. So yeah, spending all your time arguing about Catholic doctrine really is a warning sign, no matter how strongly you seem to champion the "atheist" side of the debate. Seriously.
But second, and more immediately, I wonder if anybody has advice on how to handle this, or if they've had similar experiences with their friends. I do care about this person, and I was devastated to hear this news, so if there's something I can do to help her, I want to. Of course, I would prefer most that she stop worrying about religion entirely and just grok the math that makes religious hypotheses so unlikely as to not be worth your time. But in the short term I'd settle for her not becoming a Catholic, and not immersing herself further in Dark Side Epistemology or surrounding herself with people trying to convince her that she needs to "repent" of her sexuality.
I think I have a pretty good understanding of the theoretical concepts at stake here, but I'm not sure where to start or what style of argument is likely to have the best effect at this point. My tentative plan is to express my concern, try to get more information about what she's thinking, and get a dialogue going (I expect she'll be open to this), but I wanted to see if you all had more specific suggestions, especially if you've been through similar experiences yourself. Thanks!