Yeats is worried that his daughter will grow to adulthood in a world where the old standards—the standards of the Anglo-Irish gentry that Yeats so deeply venerates—are in terminal decline. That is why he seeks to protect his daughter from the democratization of society and its values by ensuring that she will behave herself in a manner appropriate of a lady of her class.
In practical terms, this means not behaving like Maude Gonne, Yeats' close friend, who, according to him, sullied her breeding by engaging in radical political activity:
Have I not seen the loveliest woman born
Out of the mouth of Plenty's horn,
Because of her opinionated mind
Barter that horn and every good
By quiet natures understood
For an old bellows full of angry wind?
This is not to say that Yeats wants his daughter to become a woman without opinions—he explicitly states that she should be "chiefly learned." It's just that he's worried that she might turn out like Maude Gonne and display a kind of intellectual hatred for others and their opinions, which is not becoming for a lady, especially not one from the Anglo-Irish gentry. As an intelligent, educated woman, Yeats's daughter will have opinions, but she won't be opinionated.
In the final stanza, Yeats expresses his wish that his daughter will be whisked away by her future bridegroom to a place—the kind of stately home associated with the Protestant Ascendancy—where custom, ceremony, and innocence are the norm. Yeats clearly hopes that by entering such a domestic arrangement, his daughter will be protected from the storms of social change that rage outside.