I'm answering this as a committed Christian myself, so coming at it from a religious point of view, and assuming that you are, too.
Studying sanskrit shouldn't be a problem religiously - it's only a language after all. In theory neither should the Eastern philosophy. The faith and philosophy you teach at home will have more impact over the long term than their primary school.
I'm sure the school would be welcoming of all faiths, and it's also positive for your children to experience different faiths and cultures, as it means that if (as I assume you hope they will) they come to their own mature Christian faith, it will be from an informed and independent place.
However, my concern would be more about protecting them from undue confusion and (what I assume you would see) as potentially negative moral influences at such a young age. Might they get an idea that all religions are equal; that it's enough to be a good person? Are you confident in your own faith and leadership of the family to counteract those messages?
Is this the only option for your children?
You might find more detailed/nuanced advice on the religion board, unless your concern is specifically about the educational merits of Eastern traditions.