Really translates to celebrity, but follow along with me...
If people are ok with the fact that they weren't necessarily great people to those who lived outside of the Rat Pack stage life, that's fine. I'm ok with that in listening to their music, but it's hard to convince me that they are worth all the obsessing outside of the music.
It's like the way I can rationalize hollywood liberals and my enjoyment of their movies, in spite of my disagreement with their politics. 1 - I enjoy their movies or whatever art they practice (movies, music, etc). 2 - I can enjoy that and not like them as people. 3 - I can't convince other people who can't enjoy their movies or music that they should. I do enjoy the art only if I can separate that from the person. If I can't separate the art from the person, then I can't enjoy it. I don't enjoy mafia stories generally, because I can't separate the intriguing story from the horrible characters in it. I can enjoy Sinatra's, Martin's, Springsteen's, and Mellencamp's music because I can separate who they are, their politics, and anything else from their music.
Look at the worldwide love for Michael Jackson. Most people can still separate who he has become from who he was during Thriller and earlier albums. Less so with Bad. And then it all went downhill when people could no longer separate his psychological problems from his musical persona. The people who are still his most loyal fans seem to only remain that way by continuing to separate their love of the music from the love of the man. The worse his problems show through, the more this ability to love him moves from separation to outright denial. In order to still love his music, many people have to deny that he is a creepy person at best and a pedophile at worst. The more the art and the artist become one, the more difficult it is.
I think that's why love of the Rat Pack's music and lifestyle so often translate into a love of the Rat Pack - by the end, they seemed to be one and the same. The Rack Pack worked very hard either become their stage personas or to convince people that they were their stage personas. People feel they were who they presented on stage, and therefore, indiscretions outside of that image are either not really who they were anyway or are ok, because the rest was great. Was Sinatra a great guy with a great voice who did stupid things or was he only a thug with a great voice?
We all make mistakes or do things that aren't great, and our friends love us anyway. We all believe that those bad things are not who we are; we are the good things we do. How you feel about the Rat Pack itself (and possibly, but not necessarily the music) seems to fall along the lines of whether you think they were truly more of the good parts of themselves or more of the bad parts of themselves.