Trample an Empire Down, by Mack Reynolds. First published in 1978. I bought a copy in a used-book shop, some years ago, but I just barely remembered and recognized the general plot when I saw your description today, so I had to do a little Googling to figure out what the title was. Sadly, there doesn't seem to be an e-book edition available through Amazon at the moment, but, if you click on the title, you will find I linked it to where you can buy a used copy pretty cheaply. I believe this scan is from the first edition's cover art; it might ring a bell in your head?
Mack Reynolds set many of his works in near-future worlds where certain economic realities had finally been changed by modern technology so that everyone was guaranteed to be able to afford housing, clothing, necessary medical care, three square meals a day, etc. But in many cases the adult citizens could not find permanent employment --- no matter how badly they wanted to feel they were doing something useful with their lives. In other words, Reynolds liked to play around with possible reasons for why reaching a point of "everyone's basic economic needs are finally being met, all day, every day!" would not necessarily mean that a true Utopia had been achieved, and would not mean that all other social and political problems would magically disappear into thin air in short order.
This book, as I recall, was more overtly satirical than much of what he wrote -- or at least that was my impression when I first read it. (Having previously read old copies of several of his other novels.) To show that we are, in fact, talking about the same book, I shall quote a few passages which illustrate that the plot closely corresponds to what you remembered.
For instance! Your mention of one woman in the new political party whose personal agenda centered around sexual issues, and the concept of "no virgins!" (when they're over a certain age, anyway), is clearly a memory of this passage. The character speaking first is Karen, one of the founding members of what they are proud to call "the Subversive Party."
"Ummm. I've got a pile of them. I've been in revolt on matters sexual
since I was in my early teens and couldn't get satisfactorily laid
because I was jail bait. The only sex I had was in places like the
back seats of hovercars with gawky kids who didn't really know how to
Morris cleared his throat and said cautiously, "What changes did you
have in mind?"
Karen went into her ideas with a vengeance. "I feel that at the age of
fifteen every girl should be required to appear before a government
doctor for an examination. If she's still a virgin, her hymen will be
surgically removed and then she'll be given one of these new birth
control shots that last for a year. If she's not a virgin, she'll just
be given the shot."
Her visitor said, "Go on. What happens to the virgin?"
She finished her drink. "She'll be required to take on a sex
instructor, of her choice, for sex education."
"Uh, what kind of sex education?"
She looked at him scornfully. "What do you think?"
And here's a bit where an undercover agent of the IBI (Inter-Continental Bureau of Investigation) is reporting to his Chief (the Director of the Bureau) on what he's just learned about the goals and methods of the leadership of the rapidly-growing Subversive Party. The agent had been tasked with finding out if these were just some random nuts, or a serious danger to the status quo, or what, and he is now offering his evaluation.
Cliff Dix said, "Chief, this is more serious than I at first thought."
"How do you mean?"
"They're not serious."
The other looked at him, as though he was out of his mind. He said,
"What in the name of Holy Zoroaster are you talking about?"
"The heads of the Subversive Party. They aren't serious. They're just
in this for something to do. They're bored. All three of them are on
Guaranteed Annual Income and they haven't anything to do, so they came
up with this little romp. Remember you told me to read up on former
radical parties of the United States; the Wobblies, the commies, the
various socialists and so forth? Well, all those people were
idealists, devoted. They really believed in what they were advocating.
They might have been wrong, or impractical, or whatever, but they
believed in it. The same applied to revolutionary organizations in
other countries. Len and Trotsky were dedicated idealists, if we like
it or not. In the French Revolution so were Robespierre, Danton and
Marat. In the American Revolution, so were Tom Paine, Jefferson,
Madison and the rest. The nearest thing to an opportunist was possibly
The other was scowling at him. "Get to the point. And these people?"
"I don't know about the rank and file membership but the three leaders
are making this up as they go along. Their whole program. They're
taking it off the tops of their heads. By the way, they aren't a bunch
of crackpots in the ordinary sense of the word. They're all smart and
with better than average educations and intellectual backgrounds."
Hardenberg was still scowling, as though he couldn't believe any of
what his agent was telling him. He said, "How do you mean they're
making it up as they go along? What's their program?"
"It's still half-formed and most of it's fantastic, but they're
appealing to just about every element in the country from hopheads to
homosexuals. In the past, minority parties appealed to one segment of
the population or the other, to the working class, to Blacks, to
anti-Semites, or whatever. This group is trying to appeal to
everybody. They've even started a woman's auxiliary and a youth
As you remembered, the agent (real name Cliff Dix, but he infiltrates the party under the name of "Dick Oppenheimer") eventually switches sides because he doesn't like the brutal and dishonest tactics which the IBI is prepared to use to keep these people from winning an election. It seems to him that if the party is actually putting together a platform that resonates with the concerns of huge numbers of voting citizens, then the party should have its fair chance to go the distance.