The reaction some people have expressed about Carter-Silk's reported comment about his daughter surprises me too. He said she was 'hot' when she was wearing gym kit. I presume she'd have deleted his comment if she didn't like it.
Back when Diana was readying to marry Charles, her father, Earl Spencer said she was "a perfect specimen" (or something very similar to that).
To my mind there is not much actual difference except one is expressed colloquially and one is not. Both are fathers expressing appreciation of their daughters' physical perfections. So long as it doesn't go any further than visual appreciation I don't see that as wrong. Such expressions may make people feel uncomfortable but there is nothing actually wrong or harmful in a man seeing physical beauty in a woman, even his daughter, just as there's nothing wwrong or harmful about me seeing physical beauty in a man.
Parents, especially mothers, often speak of their "beautiful daughters". Why shouldn't fathers too, but expressing it in a man's way, which is anything including and between what Carter-Silk and Earl Spencer said of their daughters.
I think the real problem this whole story has shown up is the prevalence of Outrage Culture where outrage is not required. If Proudman had given C-S the sort of reply I suggested (that yes her pic was good, because it was professionally done) and he then made personal remarks, then and only then would I feel she'd be even remotely justified in reacting the way she did.
In the end, what they've both shown is a certain level of social ineptitude and it's all been blown out of proportion as if we don't all (except the Queen in her public sphere) makes social gaffs at times.