Nor the desire of women

Stop point: 101:11

"The great city" is also compared, "spiritually," to Sodom. The corruption of Sodom in breaking the law of God was especially manifested in licentiousness. And this sin was also to be a pre-eminent characteristic of the nation that should fulfill the specifications of this scripture. {GC 269.2} According to the words of the prophet, then, a little before the year 1798 some power of satanic origin and character would rise to make war upon the Bible. And in the land where the testimony of God's two witnesses should thus be silenced, there would be manifest the atheism of the Pharaoh and the licentiousness of Sodom. This prophecy has received a most exact and striking fulfillment in the history of France. {GC 269.3}

France presented also the characteristics which especially distinguished Sodom. During the Revolution there was manifest a state of moral debasement and corruption similar to that which brought destruction upon the cities of the plain. And the historian presents together the atheism and the licentiousness of France, as given in the prophecy: "Intimately connected with these laws affecting religion, was that which reduced the union of marriage-the most sacred engagement which human beings can form, and the permanence of which leads most strongly to the consolidation of society-to the state of a mere civil contract of a transitory character, which any two persons might engage in and cast loose at pleasure.... If fiends had set themselves to work to discover a mode of most effectually destroying whatever is venerable, graceful, or permanent in domestic life, and of obtaining at the same time an assurance that the mischief which it was their object to create should be perpetuated from one generation to another, they could not have invented a more effectual plan than the degradation of marriage.... Sophie Arnoult, an actress famous for the witty things she said, described the republican marriage as 'the sacrament of adultery.'"-Scott, vol. 1, ch. 17. {GC 270.1}

Nor the desire of women

To say one power is more gay than the other, I can't tell.
I'm sure not all of France was gay either.

I will admit France popularized it while the Papacy hid it, that is till recently.

And their dead bodies shall lie in the street of the great city, which spiritually is called Sodom and Egypt, where also our Lord was crucified. (Rev­ 11:8)

As you can tell by the GC quote to the left, the Great City here is said to be France.
As I showed in Revelation 11 Proof I don't put much stock in the historical quotes coming from the Great Controversy.
From the Bible it also says "where also our Lord was crucified".
That was in Rome.
Not much further into the GC you can find this quote.

Babylon is further declared to be "that great city, which reigneth over the kings of the earth." Rev­ 17:4-6, 18. The power that for so many centuries maintained despotic sway over the monarchs of Christendom is Rome. {GC 382.2}

So unless we have two great cities in Revelation you will have to choose either France or Rome.

Was there a problem with the desire of women in the Papacy?
All I can do is show you that yes there was.
The Papacy fulfills text just as much as France does.

And no desire for women could also mean Catholic Priests being celibate.