BSA doesn’t hate your daughter. You may talk to the local troop and get a feel for whether the local leaders are going to be cool or creepy. That’s where the rubber hits the road: in your pack and troop.
Even if your sponsoring body is a church that espouses traditional values, hopefully they are treating people with respect and love. I’m in one of those. Church is way traditional; but that wouldn’t affect anything that I would say or do to my boys or their families. We are all sinners, and it isn’t my place to pick “ok sins” or “bad sins.” We’re in church because we need love, grace, and rehab. Everyone welcome, and everyone included, families, too.
My sponsoring body would be hesitant to approve gay leaders, if I’m perfectly honest - which is not to say they absolutely wouldn’t. But I know the scout leaders, and they would make a point of making your family and your daughter feel welcome at pack meetings and den meetings.
Local is where the program happens.
It is fun, and there is a lot of good in scouts. Try new things, gain confidence, treat the earth with care… and so on. Plenty more good than bad, so we support it.