Mixing the World and God

The Bible is very clear about us keeping ourselves pure and separated from the World. We are to be the Light to the world, to show them the love of the Father.
Matthew 5:14 "Ye are the light of the world. A city that is set on an hill cannot be hid."
We are also supposed to be different from the world, set apart and different as a testimony to God.
Titus 2:14 "Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works."
Peculiar doesn't mean weird or strange, but different and unique. We should be a special prize that God would be proud to set apart and show off. I think of it as a peculiar vase you might find at an antique store. You're willing to pay more for it because it's different, not like the rest, and attracts attention for its good qualities.
This is a basic, easy concept to understand. And in Baptist circles we apply this concept to many things. We understand we should dress differently, we should listen to music that is holy and different from the world's music, we preach against bringing the world into our worship services, we even use these verses to purify our homes and provide a safe, nurturing environment for our children.
It's easy to understand that mixing unholy music with a Holy God does not please the Lord. It's easy to understand that Aaron and the Isrealites were wrong to make a golden calf and worship it, even though they said they were worshiping God. They thought they were doing what was right, they had good intentions. But it wasn't how God wanted to be worshiped. They had taken wrong worship and put God's name in it, and He wasn't pleased.
So why is it okay to take a pagan and worldly practice, put Jesus in it, and think it will please the Lord? Because our intentions are good? Were Aaron's intentions good enough? No, Moses had to beg God to not kill Aaron and the Isrealites. Is it okay to mix pagan practices and God's name because in our hearts we're sincere? No, the Bible says that our hearts are deceitful above ALL things and desperately wicked (Jeremiah 17:9).
Just because in our hearts we are sincerely trying to honor the Lord, does not make it okay to worship and honor the Lord with pagan practices.
Sincerity did not help Cain when he made a wrong sacrifice to the Lord. God was not pleased with fruits and vegetables when He had made it clear that a proper sacrifice was a meat offering.
God doesn't want our good intentions and what we think is right. He's already told us what He wants, and how He wants to be worshiped. And He makes it vividly clear that He does not appreciate it when we take worldly practices, and try to worship or honor Him with them. He hates it, and it does not please Him. I think it would be fitting to search and discover how God would want His birthday to be celebrated, or His resurrection, or how He would want to be worshiped with music, instead of adapting traditions that stem from a completely anti-God belief system. He is worthy of our time and consideration of how He would like things to be done, isn't He?