Probably a lot of our traditions come from pagan beliefs. The names of the week and words such as cereal come from the names of pagan gods. But using them doesn't mean we worship them.
Christmas was used by the early church to replace the ancient Roman pagan holiday of Saturnalia so converts to Christianity wouldn't be tempted to celebrate Saturnalia (and Roman holidays were a lot of fun). Saturnalia didn't "become" Christmas, it was replaced by it. There are almost no similarities between them. A lot of holidays started this way, such as Valentine's Day. It doesn't make them pagan.
The tradition of Christmas trees started in 1500s Germany.
“It is not our part to master all the tides of the world, but to do what is in us for the succour of those years wherein we are set, uprooting the evil in the fields that we know, so that those who live after may have clean earth to till." -J.R.R. Tolkien