Scenario #1: The president of a fraternity used to have a sexual relationship with one of his brothers, who is now also the chapter's secretary. They broke up at some point and were fine about things until the president's new boyfriend decided he wanted to rush and become a member. The secretary doesn't want the new boyfriend to join the fraternity.
Scenario #2: Two young women in a sorority used to be in a long-term relationship, and it ended badly. They don't like each other, won't speak to each other, and have great difficulty being in the same room. Both ran for officer positions, one winning president, one winning vice president. They still refuse to talk to each other and animosities are magnified.
Scenario #3: A male pledge educator at a co-ed professional fraternity enters into a relationship with a young woman who is joining the fraternity. The pledge educator volunteers to quit his position to avoid a conflict of interest, but there's no one interested in being the pledge educator. Instead, the members vote to remove the young woman from potential membership. Both the man (the pledge educator) and the woman (the pledge) quit the fraternity altogether rather than lose their relationship.
Out here in the post-college "real world," dating at the office is a pretty common occurrence. You spend tons of time around other available people, you get to know them pretty well, and things happen. If you've seen even a few episodes of "The Office," you know the complexities, awkwardness, and endless comic possibilities of office romance.
We should not be surprised that dating within student organizations is fairly common, also. Coed groups have dealt with this uncomfortably for years. Lesbian, Gay, Bisexual and Transgender (LGBT) students are becoming more empowered and accepted in same-sex organizations like sports teams, fraternities, sororities, etc., and the relationships are starting to happen more openly in those organizations. As a result, many of those organizations are dealing with the awkwardness for the first time, and they have no idea what to do.
Even the most accepting of members don't know what the hell to do when the sexual relationship between brothers starts going south. The founders didn't really set forth guidelines for this scenario, did they? And they sure as hell aren't doing breakouts about this topic at fraternity leadership school.
Some people say that the solution is to get rid of the homosexuals, but of course, that's not going to happen, and it's not the right thing to do. You also can't really forbid such relationships because people inevitably ignore the rule, and it's not really cool to tell people who they can and cannot spend time with.
However, I believe that it is fair to expect members to leave the drama of their relationships (or former relationships) out of the group's operations. I believe that people can have relationships with whomever they choose, and it's none of my business, until it starts affecting the organization's performance. I believe, for example, that it would be completely fair to tell those two former partners who are now president and vice president of their sorority to either find a way to work together, or resign their positions. I believe that a treasurer who would seek to prevent an otherwise eligible man from joining the fraternity because of his own jealousies or post-relationship discomfort is being unethical and unfair to the potential member.
In most cases, confronting unreasonable and unproductive behavior will do wonders. Get the two people in a room with caring brothers or sisters and talk about it. Let them know how it's affecting the chapter, the environment, and chapter morale. Tell them they are setting a bad example and endangering the ability of future gay members to be open in the chapter. Ask them what they will commit to do immediately to deal with the situation. If they are unwilling to solve the problem, they might both be suspended from membership.
You can't stop young people from wanting to be together. A progressive group would work together with their campus LGBT student group, that group's advisor, or a gay alumnus to develop a fair fraternization policy that allows people the freedom to date the people of their choice, but that also ascribes a few reasonable guidelines that protect the group's ability to function effectively. Don't be afraid that you'll be seen as homophobic for considering a fraternization policy that is fair and considerate. Ironically, it's the groups that are the most open and accepting who are probably going to confront this first.
By the way, this would be the part where I would give you a link to a perfect fraternization policy for you to modify or adopt. Unfortunately, I can't find one. If anyone has a good one, please send it to me, and I'll share it here.
In part two, I'll talk about in-chapter relationships from the perspective of the individuals involved in the romance. If you're going to do it, you'd be smart to set a few ground rules for yourself and your partner.