There's a significant difference between the GSUSA (the GSA is a Federal agency and the acronym is too similar to the BSA's; the GSUSA loathes the use of that acronym) and the BSA. GSUSA units are essentially "owned" by the local GSUSA Council. Whereas BSA units are "owned" by the sponsor. If your GSUSA Council is quite liberal, you could have an issue with the leaders they've approved, and you may find it difficult to get all the information you'd want about why they were selected. Whereas if your BSA Council is liberal, but your unit's sponsor is conservative, you'll not see the problem you fear.
And you should be aware of, and ideally involved with, your unit's sponsor as well as your unit. We do have some children in our unit who are from single-parent families where Mom (never Dad, eh?) has to work a bunch of hours and can't put much time into the unit. But if a family has the resources to contribute time to the unit, but refuses to do so, well, then I can do without their son.
If Americans expect the BSA to be a safe place to put their kids into without any effort on their part to ensure that it's units are, in fact, such safe places, then Americans are very foolishly putting way too much burden on the BSA. It was, is, and always will be the parent's responsibility to do this, not the BSA's. The BSA has never accepted responsibility for unit leaders' actions, and it's not starting now.