Why is this even a debate? You should be allowed to celebrate anything, no matter what religion. Many 'religious' holidays have taken on a non-religious or even commercial meaning now-a-days, so it's also a matter of whether you're going by the holidays' traditional sense. Seriously, why would this not be allowed?
Most common religious holidays have secular counter parts. For example christmas has Santa and easter has the easter bunny. Which makes it possible for non religious people to celebrate the holiday with no religious entanglement. They celebrate them to celebrate the new year, family, friends and the good things in life no religious belief necessary.
There is no point to not let someone who is non-religious celebrate a religious holiday. Every religious holiday has already been adopted by the entire world so to now prohibit several billion people to stop celebrating religious holidays is simply stupid. The overall point of a religion is not about honouring a day in a year but to honour and celebrate a Deity. For me as a religions person, the only thing that bothers me is how non-religious people want to change Merry Christmas in happy holidays or seasons greetings just to leave out Christ. Its your choice to celebrate a religions holiday so don't go around trying to leave out the religious meaning of a holiday. Christmas is a holiday to celebrate Christ's birth and Easter is a holiday to celebrate Christ's death and resurrection. Anybody has any right to celebrate that and add whatever crap you want like the Easter bunny or Santa clause but don't be offended when you hear Christ in a holiday name or meaning because no one forced you to celebrate anything. So in conclusion, yes anybody can celebrate a religious holiday but no one has any right to try to leave the religion out of it, suck it up or don't celebrate the holiday.
What do you mean by religious holiday? Are you trying to say that it should be illegal (for Example) an atheist to celebrate Christmas? I think anyone should be able to celebrate any holiday they want. No matter of religious or non religious affiliation. Many Holidays have taken on a non religious aspect.
People can do what they believe in or what they want to do. If a person don't believe in something such as religious holidays, I think they'll just enjoy the time off. It's a win-win. Celebrate or not, a holiday is a holiday. This question is a bit confusing but that's my interpretation of this question.