Yes, that must be it, I'm sure. It was all coincidence. She received an invitation to a Klan meeting, and everybody in her inner circle scratched their heads not having any clue how.
When Sanger founded the American Birth Control League in 1921, she was close friends with one Lothrop Stoddard. They had been friends for years, as her publication Birth Control Review gave a very positive review of his most notorious book in 1914, almost a decade earlier. (See here)
Who was Lothrop Stoddard? Among other things, he was a Klansman.
In Sanger's autobiography, she starts her section on her Klan speech as "I received an invitation", which contained a letter of instruction on where to go, etc. She doesn't specify if this invitation was random. Why did the Klan pick her? What was the connection? She probably didn't randomly meet a Klansman on a subway train somewhere and say to herself "now that's a great robe. That nice, pointy hat, I need to introduce myself to THIS guy. He is making sense!" Did the klan pick a random name out of the telephone book and say to themselves "Now this is the one!" Out of the hundreds, if not thousands of radicals they could have picked, why did the Klan pick Sanger? What was the process?
By a simple process of agreeing that sending her an invite was not random, and we have also employed a process of elimination, it has to be Lothrop Stoddard, as a Klan member(current or former/recent in the 1920's) as well as a member of her Birth Control League. Through his contacts, his extremely close proximity, I would bet you is how Sanger found herself the subject of an invitation and later speaking event for the Klan. It makes too much sense to not be at a minimum a strong possibility.
Could I be wrong? Possibly. Nobody's ever looked into this, that I can see. Were there other Klan members at the League? Could be. If so, then Stoddard may not be the missing link. I would bet, though, that there's even more of a "here" here than what I've already put together, whatever that ends up being. There usually is with progressives. These are some nasty people.