The GOP didn't know, at that time, of the double standard you mention. Or at least didn't realize how much of a double standard there was.
By the standards of the time, they thought they had uncovered a serious pattern of sexual harassment.
By the standards of the time, they thought they had uncovered the perjury trap they had been seeking since early 1992. Considering all the sexual harassment committed (and exposed, thank you Larry Flynt) by Clinton's most powerful (and harshest) critics in the House, it's no wonder that Democrats rallied to the polls in such record numbers for a sixth year incumbent off-year election.
To qualify for the term
sexual harassment said activity MUST BE UNWELCOME. Considering the actions pre- and post- said "harassments" by the likes of Juanita Broaderrick, Kathleen Wiley, and Paula Jones; plus the behind the scenes activities of semi-amateur/professional Republican political operatives like Linda Tripp and Lucianne Goldberg, it's no surprise that the American people (outside of the majority of registered Republicans, who at the time either didn't care or had been too inculcated/indoctrinated by the propaganda of the Vast Right Wing Conspiracy[SIZE=-4](tm)[/SIZE]) didn't believe them or the "purity"

of their motives, or the motives of people like the House Impeachment Managers.
Though I don't deny that Clinton was guilty of sexual harassment (1); based on the existence and testimony of the Jane Doe's, who clearly did NOT seek fame and fortune, vengeance, or political hatchet work in favor of the Republicans. And kudos to then Congressman Lindsey Graham, who showed that while he was a True Believer, his votes (two for, two against the four introduced articles of impeachment) showed he was no political hack. And the only one I could say that of among the 13 House Impeachment Managers. Probably explains why he got elected to a Senatorship in South Carolina, AND why the Tea Party seems to think he's a borderline RINO.
1) It just simply wasn't something worthy of turning the course of the history of Western Civilization. High Crimes and Misdemeanors had always been thought to mean actions committed
in the performance of one's office as President, not in one's private life, or before entering office. If the Supreme Court had not fallen flat on their collective faces by making their ridiculous 9-0 ivory tower thinking decision declaring that the President "would suffer no undo distractions by being forced to face civil suits while in office" none of this would ever have happened.
Does anybody think that the Susan Carpenter-McMillan branch of the Vast Right Wing Conspiracy[SIZE=-4](tm)[/SIZE] would have continued Paula Jones' suit if it couldn't be enacted until AFTER Clinton left office? It's no coincidence that Judicial Watch and the American Spectator had their funding yanked by their uber-right wing billionaire backers shortly after W was sworn in.