What Scriptures are used to advocate the Holiness teachings of the groups like Nazarenes and Wesleyans?
I do not know what they understand about holiness, plus I would say individual members can have different ideas . . . maybe what they discover as they grow and mature as children of God, while others might not be truly saved and might have mainly doctrinal ideas.
demanding that people be sinlessly perfect.
It depends on what you consider to be sin. There are people who are very into do's and don'ts, while others are concerned with how to relate in love, and others can be about what is right in feelings and emotions, and others are concerned with how our character . . . our nature . . . is becoming. I would tend to go with holiness being about God changing our nature so we become like Him in His love > 1 John 4:17.
many Christians are too worldly
If we count on ourselves to develop our ideas and ways, we will become more and more worldy . . . either giving in to lusts for pleasures and convenience, or congratulating ourselves that we are so right and with this comes looking down on others.
Holiness of God's love includes how we have become immune to sin-sick drives and interests >
"And those who are Christ's have crucified the flesh with its passions and desires." (Galatians 5:24)
And holiness of Jesus love makes us humble . . . not conceitedly looking down on anyone else, but being strong with compassion >
"He can have compassion on those who are ignorant and going astray, since he himself is also subject to weakness." (Hebrews 5:2)
I want to see holiness promoted in church without being legalistic or holier than thou.
What matters is if we present what really is holiness.
My personal understanding is something like this >
First, a person trusts in Jesus, and he or she is joined to Jesus >
"But he who is joined to the Lord is one spirit with Him." (1 Corinthians 6:17)
Faith includes our actual union with God. And in our union spiritual with God, His grace includes the effect of His almighty power of His love in our nature >
"Love has been perfected among us in this: that we may have boldness in the day of judgment; because as He is, so are we in this world." (1 John 4:17)
Included in the process of becoming holy, then, is how God's love cures our nature. Also, Hebrews 12:4-11 says that God's correction makes us become
"partakers of His holiness". This fits with how being
"one spirit with Him" (1 Corinthians 6:17) has us sharing with Him in how He is holy. And God is holy in His way of loving, which is so superior to and better than how we humans have loved. We become
"as He is" "in this world" (1 John 4:17), because of how His love in us perfects us and makes us holy in love. This includes how we become pleasing to our Heavenly Father > in His gentle and quiet love >
"rather let it be the hidden person of the heart, with the incorruptible beauty of a gentle and quiet spirit, which is very precious in the sight of God." (1 Peter 3:4)
So, we trust God to make us deeply and pleasantly quiet and humble. And in His quietness and rest we share with him in His own almighty immunity against any and all sorts of fears and personality torments and pleasure lusts and selfish ways of reacting to not getting pleasure and convenience. Instead, we share with God, and do not give in, also, to boredom and loneliness and depression and bitterness and hurts which would violate us and degrade us from being quiet and sweetly and sensitively sharing with God in His love.