Historically, certain Christian denominations were not always very subtle in regards to their views on things, and I would think that G.K. Chesterton used "hate" as a stretch to get his point across that many Protestants are/were ardently against praying to Mary, and in many cases, were very nasty about it. (Please note, I am using the word "many", not all).
The battle of Lepanto occurred in 1571, during the Reformation (when things were at their worst), that is perhaps why he used hate, as many Catholic Churches were forcibly taken by state governments, and many statues, such as those of Mary, were smashed.
I can't claim to be an expert on this, but those are my thoughts on why he used such language. I agree with you that no denominations have expressed hatred towards Mary, but certainly there have been individuals within those denominations that have expressed such, that includes heretical Catholics as well.
Thanks for your response. I was generally aware of his religious background and your theory makes sense.