It's a woman's changing room, not a whoever-you-like-seeing changing room. There is no reason (other than some sort of puritanism) to get freaked out about girls seeing penises. In this context, it's just a body part.
The idea that only uncivilized societies allow for public nudity is an ignorant and self-perpetuating colonialist stereotype.
Not wanting eg your wife to see a penis, especially a feminine woman's penis, is laughably insecure at best, and bigoted and hateful at worst.
Similarly, not wanting your assumed daughter to see a penis is harmful to her (or potentially his) emotional growth, and should be considered borderline child abuse.
You are putting many words into my mouth - for starters I didn't mention anything about uncivilized societies. Second, you don't get to decide what a women does and doesn't want to see - especially if you're a man. As it turns out many women and girls would be uncomfortable around male genitalia when in a changing room for women. I suppose you would be OK sending a girl "d*k pics"? What would your excuse be? "Don't be so insecure!!!"
This is totally asinine. There are a many reasons why... With just a little thought I'm sure you can think of at least one.