Lesson 1: Henry A. Kissinger said "If it's going to come out eventually, better have it come out immediately."
Yes, you can run for office if you have an unusual past or lifestyle--but not if it's a secret. You have to "pre-spin" your own story. The best example of pre-spin is Pat Buchanan's 1992 Biography "Right from the Beginning" in which he explains that he would be a great President because of his youth spent as a binge drinker who wrecked cars and got into fights with police officers.
It might be ok to be a gay Republican Sheriff running for Congress--although you risk inevitable Village People comparisons--but you had better not surprise folks with it. Sure, in the old days you could run from the closet, but not in the era of blogs, Facebook and Twitter. We all knew that Babeu was gay, just like we all knew that Jim Kolbe was gay. But Kolbe managed to hide it for the first 12 years that he was in Cogress while Babeu managed to keep it quiet for like a week after he announced. (Kolbe actually faced more serious and more credible allegations than Babeu in the early 1990s, but without blogs and with Kolbe's connection to the Republic, he was able to keep things from exploding.)
Lesson 2: Conflicting Bases
When I was a kid, the big fad was "Do It" shirts--you may remember "Teachers Do It With Class" etc. It seems like there was one for every profession and I remember going to Tucson Mall and seeing an untouched stack of shirts that said "Preachers Do It with Amazing Grace." Naturally, they had not sold one of those shirts. Why? Well, you can only wear it if you are a preacher--and if you are a preacher, you can't wear it. The shirt had mutually exclusive target markets. In order to buy it, you had to be two things and those to things conflicted.
Politics has the same marketing requirement as T shirts. When you are assessing your political chances, you have to see how big your base can get. So you can be a gay Democrat, but you can't really be a gay pro-life democrat. You can even be a gay Republican if you market yourself as pro-choice, moderate, sophisticated and urbane. Then you have to pick a swing district in a university town--use Jim Kolbe as a case study.
You can be a tough, law and order, secure the border, build the dang fence, never without your Glock, Republican candidate running for Congress in rural Arizona, but that base is going to be put off by the gay thing--and that's not just because he's gay; it looks like he has a reckless, secret life. Babeu may still have a supporter or two, but his base is gone.
Lesson 3: When it's over...it's over.
Not only does he have no base, but he's flanked by Ron Gould who appeals to Babeu's former base. Gould is also a tough, no nonsense, rural, secure-the-border type--running against Gossar...a Flagstaff dentist who dutifully votes with House Leadership.
Gould's weakness is that he can't raise money--his endless series of No votes has won him few friends and he's running against an incumbent. Ironically, however, Gosar is also weak at fund raising and is decidedly unorganized--and after Redistricting, Gosar has quite a few new constituents who will be eyeing him for the first time. Most of those new voters will go for Gould.
If Babeu stays in the race, he may serve as spoiler for Gould--or saviour for Gosar depending on your perspective--but he won't get into double digits and he will spend the next 6 months being hounded and further humiliated by the media.
It's time for him to go.