No excuse is required, religious or otherwise, and it should not be automatically assumed that everyone is expected to go.
For example, in my case it's nothing personal but I just don't want to spend time with you. I want to go home instead and do something interesting.
The religious aspect may indeed be the reason, but that is not really relevant to your concern. Even without religious motives, people do not need to attend special celebratory events. It is not mandatory.
I do not go to such work sponsored events. My reason is that I simply do not want to. I don't go to company picnics or holiday parties. I do not go out to the social gatherings for a drink after work. I avoid all of those things for the simple fact that I just do not want to attend them.
My reasons for not wanting to attend a company sponsored event are my own, and they are none of anybody else's business. I will, however, mention some here so as to remove the veil...
As much as I may like some of the people at work, I don't go there because of them. I don't go to socialize or to have fun. I do talk to people sometimes, sometimes about fun and interesting things, but that's not why I'm there. If it weren't for the fact that I need money to pay the bills, I would not be there at all. That is true for most people.
If I am not working, I want to be home teaching my son something cool or playing Minecraft or World of Warcraft with him or whatever he is into at that time. I want to help my daughter learn to swim or skate. I want to watch a movie with my wife.
I do not drink alcoholic drinks socially, nor do I drink coffee, and I have low expectations when it comes to food, and I do not care about football, baseball, or Nascar; so the bar does not interest me, nor do restaurants, nor does 90% of what my co-workers want to talk about, so when I am not working I do not want to be wasting my time drinking a soda or eating something fancy or talking to people whose interests are boring to me. Nor do they want to hear me talk about what I'm interested in; I could talk for a half hour about the fine art of lighting a fire in the rain with flint and steel, but most peoples' response is "Why didn't you just soak it in gas and drop a match on it?"
I can understand asking someone who usually does go to such events but misses some specific ones. If I usually did go to them but skipped the Christmas party, I would understand you asking what's up. But if I just don't go to any of them, then it seems like you're trying to pressure me into going - some people actually do that, and I have been pressured into going to events that I really did not want to attend, and I have sat there bored for over an hour just waiting until I could politely leave you. That is well beyond rude.
When I do find a specific person at work who shares common interests, then sometimes I make friends with that person outside of the work setting. In general though, I do not want to attend your events, and it gets annoying when people keep asking why I don't go, as if I have done something wrong. I didn't go because I didn't want to.
So, how does this answer your question? Like so: The best way for you to give your co-worker the opportunity is to just keep doing what you are doing; that is, let them tell you if they feel like it. If you really have no good reason to inquire and you just feel like the person should be there, then just leave it alone. If you have some other reason for concern and you do try to coax out my reasoning for not attending, please be very considerate when doing so as to make sure that I do not feel bullied.
It might help if you make your intentions known up front about why you even care, such as "Hey, I noticed you don't go to the company special events and was wondering about that. I'm not trying to be pushy, but if you want to go and feel like you can't we'd like to help you work things out." Then I can answer simply "Thanks for the offer, but I just don't go to those things." Or if there was some roadblock you might hear about it and be able to help, ex: "I just can't make it because of my kids," then you would have the option to try and push for more kid-friendly activities if you wanted.