By itself it is hard to say as we don't know why men and women feel that way about her. Before I clicked on the link my initial way of reading this was that she was acting in a manner men would approve of and women would really hate. Based on this I saw it as mainly disparagement even though the following text makes it clear it's mainly praise of her beauty. I don't find it very well written myself. It's quite a clumsy sentence to read to me and slightly confusing.

A little of both, it implies: - she is beautiful, so most men would have no choice but to approve in that way The second part for women seems to imply: - women would be jealous of her beauty, and therefore dislike her

This says that men will approve of Lydia and that other women will immediately despise and vilify her. "at least somewhat" = "to some degree, but not necessarily completely".