You don't have to lie to still allow the SC presence in your house if you want. You don't even have to couch it in the religious part of it - but talk about the historical figure of Nicholas who used to leave coins for poorer families. And this tradition of giving is continued worldwide to this day. Some people get more excited by it, some people have big stories around it, but really, it's all about lots of people copying a nice thing to do for your fellow man in the depths of winter.
Quite how to put that in 2 year old language, would give me more than the few minutes I have now -
But if you don't want to allow the SC presence into your house at all, then that is your own family decision in any event. (And just be aware it WILL come in through decorations, tv, music, craft things in school, kids talking etc).
Our DD is in a multi denominational school, where they don't learn religious catechism in school. They do have religious education, where they learn about all faiths and cultures (or at least 5 or 6). The annual PTA money raising event that time of year is "Winter cards" that all the DCs design. They celebrate Diwali, Christmas, Hannukah, and I don't even know what else. And we also celebrate yule in our house as well as Christmas. SC is big in ALL the DCs artwork, even when it is not lead by teachers and including all those who are different religious backgrounds or none at all.
So you may avoid it for a couple of years while your DCs are small, but be prepared to answer the questions in time to come. And it doesn't have to be answered by lying.
(And if I answered all the questions with the truth in our house, I would often not get to work, I would never get out for parent-time with DH or others, I would never get to the gym for a swim for my own exercise needs, and I would never be let go to the supermarket on my own. DD goes out a lot with just me or me and DH - we don't abandon her at every opportunity. I occasionally have work events at night. I occasionally want to see my aunts, and friends who work also and have grownup conversations. I need to lose 2 stone and get back to being fit. While teaching DD about money and budgeting and organization and allowing her to choose foods sometimes is vital, there are days I need to do it fast or without a constant refrain in my ear about what she will and won't eat, and not looking to fill the trolley with treats too. And I occasionally need a break from her ADHD/aspergers issues. So I don't lie for the sake of being mean to her, but for the sake of all our sanity.) While she made her FHC last year, (she does catechism outside of school), we do have indepth discussions about lots of stuff, including the truth of religion and philosophical issues, and lots of things that many feel are not appropriate to tell her the truth about - even death (and I don't do heaven, but tell her that some believe that, I don't, but that the person won't come back either), and things like real words not gibberish (when a baby) or not using nicknames for bodyparts but the real word.