Gift etiquette for a small mixed-religion office/company?

I work in a small company and was thinking of giving some Christmas gifts (like mince pies or something else that could be bought in a nice package and shared with families) to co-workers who work close to me but are lower in rank. A couple of them celebrate Christmas too but the other two are Muslims. How (in)appropriate would it be to get them something?

At the workplace there are other three people who are higher in the hierarchy as well as the owner, all of whom are not Christian either. I don't think I should get them something, would you agree?

PS: I am new at the office, so I am not particularly close to any of them, but it is a friendly office environment.
PSII: Gift ideas or suggestions are very welcome!!!

I guess maybe I will get muffins and chocolates for everyone, like a small gift and just go around to talk to everyone during break time to share the muffins and have a chat. If anyone asks, then just reply that it's for the holidays, not just christmas, but the new year as well and a show of goodwill.

I think it would be perfectly acceptable to give a gift, especially if it's just food. You can explain to your non-Christian coworkers that Christmas is about giving, not receiving. So you are practicing your religious holiday by giving, and they don't have to be practicing to receive. If they refuse the gift, even politely, you should smile, tell them you understand, and take the gift home with you.

You could give them a gift and say something to the effect of "it's just a little something for the holidays." Don't name any one holiday in particular, but leave it open to include everyone.

Check out any proposed food gifts as far as dietary restrictions go, but other than that, it sounds fine.

However, getting individual gifts can be a little daunting, because people get sucked up into the "oh, I've got to give a gift in return" sort of thing. How about springing for a festive breakfast for the office, instead? Breakfast is cheaper than lunch, and you can have different breads, juices, etc. Everyone gets to participate -- everyone is happy. It's a win-win.

New in the office and not close to them.....don't do it. Just don't. Wait a year and see what the dynamics of that office is.
I'm Christian but I can sense that the wrong actions on your part might be taken as evangelizing by some and held against you.

It's fine with the pies idea and it's fine to give to the Muslims as long as there is no lard in them.

It's not necessary to gift to those in the higher hierarchy.