But the Christianity in the Handmaid's Tale isn't like the Christianity we have here though

You're right. It's a dystopian novel which means the religion described in the book is different to the religion that you have at home. However, Atwood uses many biblical references throughout the book, so although it seems crazy different, actually everything to do with religion comes from a source. So Abraham in Genesis had a handmaid because his wife Sarah couldn't have a baby. So really, although we know that Christians nowadays would not accept a husband having a 'handmaid,' biblically, and therefore in the Christian religion, it's acceptable.
Have a look at these things and try and find an example for them in the bible for me. Cutting off fingers for women reading, wearing something that covers the handmaid's face, men being in charge of society.
Some things of course are not inherently Christian, such as the clothes they wear, which are more for dramatic effect and scene setting, however, the colours have some significance.
All religions can be interpreted and seen in so many ways, think of how many types of Christianity you can think of, orthodox, catholic, Pentecostal etc., and this book really highlights the dangerous elements of all religions, they can very easily be twisted and manipulated to meet someone's need.