Oddly enough, this question has become somewhat politicized. People who say HAPPY HOLIDAYS might be accused of being too liberal, polically correct, etc., while people who say MERRY CHRISTMAS might be accused of being too exclusive, or just assuming that everyone is a practicing christian. So, in the end, you should just say what you feel.

Most people just say “Merry Christmas” but because some people celebrate other holidays, it’s safe and perfectly normal to say “happy holidays” instead

It depends, happy holidays can go for any special occassion, it does not have to mean Christmas. And Merry Christmas is just for Christmas time. We use Merry Christmas all the time and for the other holidays like new years or other celebrations we use happy holidays. For me personally i use; I wish you a good (whatever holiday) I wish you a good new years, i wish you a good national day etc.

I live in the UK. My view is that 'Merry Christmas' is still the norm.