Banning gay seminarians won’t end gay priests
It might make things worse.
Perhaps I should start with the obvious. Gay men can be priests. As a theological matter, it is possible for a man to both be what we identify as “gay” and to be a priest. Otherwise, any priest who “came out” would be declared invalid in all of his priestly ministry, from beginning to end. Nothing about being “gay” or “homosexual” or “same-sex attracted” intrinsically prevents a man from being a priest. Homosexuality isn’t a theological or canonical impediment to ordination.
And yet we might ask whether “gay” men ought to be priests. And, on a related note, should we ban gay men from entering seminary or being ordained? We know that the majority of recent clergy scandals have involved priests abusing other men. Would banning gay seminarians help to prevent this? And how would such a ban work?
The first difficulty involves the screening process. Of course, we could easily weed out seminary applicants who were public about their homosexuality or who openly argued against Church teaching on sexuality. But what about the people who don’t openly share their inclinations? Or the people who may have had a romantic or sexual relationship with another man but decided it was just a transitory interest? Or what about the people who had simply never been in an environment where these questions came to the personal forefront and who may not be actively aware of attractions to other men?
What would be the test for “homosexuality”? How would you know? And sometimes, how would that person know? And what happens when someone makes it through seminary and, after ordination, discovers an attraction to other men?
And then there’s the problem of change. What about people who mature or change in life and develop new attractions? Our desires and longings change and develop as we get older and have new experiences. Growing up, tomatoes made me gag, but after a semester in Italy I now enjoy them. Sexuality can be like this too. New experiences open up new parts of ourselves, and new contexts elicit new responses. Sexuality doesn’t exist in a vacuum, but in a relationship of the subjective self and the external environment. 
Then there are all the psychological walls we put up to hide our desires. My little cousin once insisted that he loved mint but hated peppermint. So my siblings and I gave him a piece of gum. After he started chewing we told him, “It’s peppermint.” He made a face and said he didn’t like it. Then we said, “Just kidding, it’s mint.” “Oh… ok, I like it,” he said. He had certain notional commitments, and he adjusted his reactions to things based on those commitments, rather than what he actually felt.
Our sexual desires can be like this as well. There’s a reason why boys in high school (and college and beyond) tend to like the same girls. Because we often take our cues for acceptable longing from others. Every gay man knows what it’s like to play along about finding a woman attractive, and many of us thought we found women attractive in the same way our peers did (especially those of us who thought being gay was a terrible thing). We only realized the difference of our longings when we better understood our attractions to other men. But not everyone gets there.
What do you do with that seminarian, the seminarian so prejudiced against homosexuality that he can’t even recognize his actual feelings? What do you do with that person, whose prejudices can harden into callousness as he seeks to cover over what he feels? Surely that will enter into the ways he ministers to those with same-sex-attractions, preventing true compassion, mercy, and engagement. He’s never practiced these towards himself, so he wouldn’t be able to fully practice it towards others either. One day he may be overcome by his repressed desires and begin acting out in odd ways, ways that he doesn’t understand and can’t face because he’s spent so much time telling false narratives about himself (to himself).
One of the most bizarre episcopal interactions I’ve ever had involved a dinner with a bishop and a group of young men. The topic of the diocese’s clergy abuse lawsuits came up. In response, the bishop cooly made a single remark, about how some people (referring to the plaintiffs’ lawyer) are just out to get the Church. I thought the remark was odd, in that it demonstrated no remorse or recognition of victims. A year later, allegation after allegation emerged against that bishop, which he flatly denied. If the allegations are true, the dinner remark makes sense. If he couldn’t adopt an integrated approach to his own failures, he wouldn’t be able to do so for his diocese.
Worsening the situation
In these situations, a hard ban on those with such same-sex desires may actually make the situation worse. Because there’s no good way to screen for this, and because the anxiety that can be associated with such desires will make it hard to address and form honestly.
And it opens a very large door to abuse. For young seminarians who may have those desires but have not really addressed or recognized them, older manipulative priests may recognize this and invite them into their lives, eventually surprising them with a carefully crafted seduction or assault. Seminarians unaware of how to relate to these desires and unable to recognize such advances (probably because they have been unable or unwilling to recognize much about sexuality generally) will be caught off guard and unable to formulate a response until it is too late.
Then, once the seminarian realizes what has happened, a mixture of shame, fear, and desire to serve the Church may prevent him from being open about what happened. The manipulator will know this and will use the fear and secrecy created by a callous ban to further manipulate. I suspect that this is a narrative Cardinal McCarrick and Monsignor Anatrella knew well and used. 
Then the seminarian will both be stuck in an abusive relationship and will be unable to honestly and vulnerably address great portions of his interior life. Far from ending gay priests, a ban creates a situation in which they’re easier to abuse and afraid to seek help. Abusers thrive most of all in environments of secrecy, and maturity stunts in the places we hide.
And here we are. Welcome to 2018.
 Though change is limited. The most serious studies have shown, for example, that while we may experience some movement in our experiences along a spectrum, efforts through psychotherapy and prayer to achieve “orientation changes” have proven largely unsuccessful.
 Regarding orientation and abuse: In 2010, researchers at the John Jay College of Criminal Justice completed a report at the request of the U.S. bishops which found no statistical evidence that gay priests were more likely to abuse minors. The report can be found here.
I believe that one of the reasons why we struggle to effectively respond to these crises are the many Catholics who stay committed to prejudiced and poorly substantiated claims, such as the claim that gay persons are more likely to abuse others and that homosexuality is the primary cause of abuse. If you want to argue otherwise, please also share the research. I’ll direct you to the study referenced above, or other studies conducted by professionals. And I won’t stand for the argument that it’s just conducted by evil liberals/conservatives/whatever. If something is wrong with the study, please show me what that is. The rest is laziness and status quo.