The BSA has always acted as the youth ministry of the LDS, has that ever been an issue?
(Addressing this specifically, before moving on to the general)
Not always, but for the last 106 years, and ending this Dec 31st. This for BSA, and LDS congregations consist of something like 20% of the troops.
The break up between LDS Christians and BSA is one that is GREATLY celebrated in LDS Christian congregations. There's many reasons for this:
1) LDS Christians feel that BSA in it's current form does not remotely provide a good youth program. An example from my own congregation is that the Scouts and the leaders went to a regional BSA conference, and the BSA leaders handed all of the boys condoms as they got off the bus. MAJOR problem for LDS Christians, who are very much against pre-martial sex.
2) Even if we overlook the difference in values, time commitment / goals of the BSA program are different than the resources and interest majority of LDS Christians have, both the kids and the adults. It's just not a popular program for subject matter or it's personel demands.
3) All of the above + human ego caused major political rifting between BSA and LDS Christian leadership.
4) And Boy Scouts of America doesn't work outside of USA. And as a global church, the LDS Christians needs a global program that works just as well in Zimbabwe as it does in Alabama.
Speaking personally now: I despise Scouts as a Church program. My congregation even asked me to help out, and I tried until... I just was too disgusted and had to formally quit helping out-- and that's after 2 meetings. I just... no, it does not work for a Christian youth program. It's fine for people who want to do Scouts, but not for a Youth program.
And that's all overlooking (formerly Boy) Scouts of America's identity crisis as it can't figure out wants to be. I really want nothing to do with the program.
Does the sexual abuse issue in the BSA help you realize that the issue occurs in all large institutions and needs to be taken seriously by everyone, not just Catholics?
That's just a "no duh" in my view. Predators exist everywhere. It's not just in churches, let alone one specific denomination.