We should worship and serve God in Spirit because it takes faith, not works, to please God.
God is Spirit, and He only can be accessed through what is done in the Spirit. We cannot correctly serve Him by our flesh (John 4:24).
The old covenant was a contract between God and Israel. God promised to do His part of the contract if Israel would keep their part of the contract. That covenant failed because Israel could not meet the terms of the contract.
God knew that Israel would fail to keep the contract even though they claimed that they would do everything God would command them to do (Exodus 19:5-8). God decided to introduce a system that would still allow Him to bless Israel even though they did not keep their promise. He said they must shed the blood of an innocent animal whenever they break the covenant.
By this act God was showing what He was going to do for the whole world when He sheds the blood of His innocent Son; He would be able to treat the whole world better than it deserves. After Jesus died in our place God stopped dealing with us according to our sins (Isaiah 54:9 & Hebrews 10:16-18).
God now deals with us according to our faith in what He did for our spirits. The spirits of the believers are treated like Jesus would be treated if He was still on earth. Hence God wants us to serve Him in spirit because in our spirits we are perfect and our service is acceptable before Him.
God no longer condemn us for the sin that may be in our flesh but He empowers us to overcome that sin (Romans 7:13-25 and Romans 8:1). Our consciences, the society, and the devil will condemn us but NOT God because He declared an end to sin’s control over us by giving His Son as a sacrifice for our sins (Romans 8:3).
When we serve or worship God we must do it with full assurance of faith, not because we do not have sin, but because our guilty consciences have been sprinkled with Christ’s blood to make us clean, and our bodies have been washed with the redemption that Jesus provided which was revealed to us through the Word of God (Hebrews 10:22). We have been set apart for God and perfected forever (Hebrews 10:10&14).
Because you have faith in the finished work of Jesus Christ worship God with a clear conscience and you will see Him transform you (2 Corinthians 3:18).