You can love and respect someone while thinking that that one belief is really stupid
I completely agree! However, it is entirely irrelevant because the original claim wasn't that they thought someone was stupid. They said they actively thought less of them and then mocked them for having the permanent mindset of a child. Your point doesn't cover that level of immature hostility.
You cannot claim to be a friend of someone while openly believing they are less than you and mocking their entire mental state and world view. The behavior is contradictory to what a friend actually does. You are not a friend in that case, you're just a shitty person who is pretending to be someones friends while (no matter what you say) treating them less than you would treat someone like yourself.
The Eugenics Wars happened with a bunch of genetically modified super soldiers that were created through selective breeding. The term 'Eugenics' often just gets used as short hand within the Trek universe for all types of Genetic Modification in general as genetic modification is illegal in the Federation.