When groups like the ACLU have pushed issues via lawsuits its often with a very specific, media attention perfect client like Rosa Parks who cannot be vilified or attacked for a past criminal record or documented issues with society and law enforcement. Not because those people don't deserve representation but because their cases were too easy to strike down and prevent progress on the underlying issue. We see this today with so many validating the killing of George Floyd because of a past criminal record or recent behavior without eve considering if those actions deserved a death sentence or night in jail. It's sad but it's true.
The Swedish rape case would have made it more difficult for the US to extradite Assange, as that case would have had priority in the UK (since it was first in time, and more importantly, actually proceeding when Assange went into isolation), and Sweden is less likely to extradite to the US than the UK.
When groups like the ACLU have pushed issues via lawsuits its often with a very specific, media attention perfect client like Rosa Parks who cannot be vilified or attacked for a past criminal record or documented issues with society and law enforcement.
I see that you are unfamiliar with the actual history of the ACLU, which has also defended neo-nazis/white supremacists, Larry Flynt, self-described terrorists, and other degenerates in precedent-setting cases.
This ignores the 30 times Assange offered to be extradited to Sweden if Sweden provided some assurance that they wouldn't extradite to the US. It also doesn't account for the incredibly strange ways the case was handled, like Assange checking with prosecutors for permission to leave the country, and then those prosecutors issuing an arrest warrant the day he left.
And regardless of whether or not you believe that, if he had been extradited from the UK to Sweden, the UK would have to consent to the onward extradition to the US. He would've had the ability to fight it in two legal systems, both of whom would have to agree the extradition were legal, rather than just one.
So while things got a little better later, it looked very bleak at the time.