Women athletes should be able to compete in any men’s events and vice versa if the opposite sex does not have their own league represented in the sport. Example, I wouldn’t think it would be necessary for a WNBA player to play in the NBA but NHL, sure. NFL, why not.
I am all for girls playing whatever sport they feel like, I really do. However, when a particular branch of sport is designed to include matches which consist only of, girls should not be able to take part in something that is only for boys, especially considering there is a girls hockey option. There are countless times boys and girls play together which is wonderful, however there is nothing wrong if boys play with boys and girls play with girls.
So no, girls shouldn't participate in boys hockey when it's not meant to be for them.