Livestrong did provide some funding for research, but that stopped in 2005 as Famm's article said. They also continue to help people cope with cancer and have various support programs for it, but again that article indicates that the majority of it is farmed out to other organizations. For the most part, Livestrong's mission is to raise "awareness" of cancer and little else, and has been for the better part of the decade.
Everyone heard of cancer? Yeah? Well, I guess we can shut it down now.
Seriously though, I think it's going a bit far to say that Livestrong is a "complete piece of shit", but that Outside article did lay out what it is and what it does. 10% of it is about raising awareness about cancer and helping people deal with it. The other 90% was marketing/PR for Armstrong, unfortunately. Your money would be put to much better use donating to just about any other cancer organization.
I'm not clear on what middle ground you seem to think that athletics in general is on. Athletes are regularly banned for incredibly minute quantities of PED's/substances that they inadvertently ingested with supplements and hair growth formulas and shit. It's not possible to test for "EVERY possible PED" because the dopers will always be a step or two ahead, like with EPO back in the late 90's and early oughts. Am I missing some PED that athletes are allowed to use or a blind eye is turned to?
I agree that the North American pro sports leagues are an exception to greater and lesser degrees (some have no off season testing, or allow heavy doses of painkillers or cortisone and the like). But most other competitive athletes are tested like fucking crazy these days.