Easter is mentioned in the Bible and I think you are correct that it's roots are Babylonian...it has been a while since I studied it.
The long story of how Christmas started is a wonderful story and though it is steeped in paganism, it has spread pretty much over the face of the whole planet pointing to the time when the Messiah, the Savior or mankind, came to die for us.
The holiday time is appreciated, and real Christians like me do not mingle paganism into our actions at home or our gatherings at church. We do go out on Halloween and set up a booth in the city, passing out candy, coffee, donuts.....and gospel tracts as we try to get people to hear the gospel, the good news of what Christ did for us so that we can have eternal life.
I'm repeating myself a lot for you....I want you to know this is real and it is worth it to have your life changed by God. His life instead of my life, He lives in me and I will be like Him perfectly forever one day soon.
What I consider true Christians are those who have conceded that they have no right to live and cannot justify their existence outside of the fire of Hell, and they have admitted to God that they are sinners who deserve His punishment, and they have believed on Jesus Christ who died for their sins and rose bodily from the dead to save them from Hell....they have received Christ in reality by faith as He is, the Living God the only Savior and they are born of the Spirit of God who is Jesus Christ living in them. They speak to God as their Father, they are joint-heirs of Heaven with Jesus Christ, and they are my brothers and sisters in the Lord.
If they do not believe the Bible, I doubt that they are Christians and I hope I am wrong....though I do believe there are some true Christians which engage in pagan methods on so-called "Christian" holidays.
The Bible commands only two commemorative ceremonies for Christians......The Lord's Supper and baptism by submersion after a person has truly believed and received Jesus Christ as their Savior. The first alludes to what Christ did for us when He died in our place, the second identifies us publicly as followers of Christ, buried in baptism in the likeness of His death, and raised again to walk in newness of life.