In general I would frown on any employees, but in particular a manager, getting into a shouting match, homophobic slur or otherwise. In a manager I would find this particularly disturbing, because you should really be promoting managers based on leadership qualities, and shouting at your subordinates doesn't display leadership, it displays bullying. As to a specifically homophobic slur, like it or not, we live in a litigatory age, and, as you point out, if the staff member being yelled at were gay, then your manager has crossed a realm into pain. As others have pointed out, this kind of culture comes down from the top. Good sound senior management would not allow the workplace to behave this way.
The fact is that in any workplace, but particularly a large one, you're going to have conflicts, and on occasion they may get out of hand. I agree that the homophobic slur is the least serious of them, but it still isn't something that should be tolerated. An off the record warning would be exactly how I'd deal with that as well, but if the employee persisted in that sort of conduct, then it would have to move on to a more formal disciplinary process.
Oh, and to all those brave alt-right haters, want to end up in court, go tell a subordinate who complains they were threatened or abused to suck it up.