Lets take a closer look at what Paul said...
Rom 12:1 For this reason I make request to you, brothers, by the mercies of God, that you will give your bodies as a living offering, holy, pleasing to God, which is the worship it is right for you to give him. Do not conform yourselves to the standards of this world, but let God transform you inwardly by a complete change of your mind. Then you will be able to know the will of God---what is good and is pleasing to him and is perfect.
Joh 4:24 God is spirit, and those who worship him must worship in spirit and truth."
This truth is repeated by James in this passage:
Jas 1:27 What God the Father considers to be pure and genuine religion [ceremonial observances]is this: to take care of orphans and widows in their suffering and to keep oneself from being corrupted by the world.
If you continue to read the Romans letter you quoted from, you will find what "presenting your bodies as a living sacrifice" and "worshiping in Spirit and truth" entails ...note there is not even the slightest reference here to "appearance"
Rom 12:9 Let love be without deceit. Be haters of what is evil; keep your minds fixed on what is good.
Rom 12:10 Be kind to one another with a brother's love, putting others before yourselves in honour;
Rom 12:11 Be not slow in your work, but be quick in spirit, as the Lord's servants;
Rom 12:12 Being glad in hope, quiet in trouble, at all times given to prayer,
Rom 12:13 Giving to the needs of the saints, ready to take people into your houses.
Rom 12:14 Give blessing and not curses to those who are cruel to you.
Rom 12:15 Take part in the joy of those who are glad, and in the grief of those who are sorrowing.
Rom 12:16 Be in harmony with one another. Do not have a high opinion of yourselves, but be in agreement with common people. Do not give yourselves an air of wisdom.
Rom 12:17 Do not give evil for evil to any man. Let all your business be well ordered in the eyes of all men.
Rom 12:18 As far as it is possible for you be at peace with all men.
Rom 12:19 Do not give punishment for wrongs done to you, dear brothers, but give way to the wrath of God; for it is said in the holy Writings, Punishment is mine, I will give reward, says the Lord.
Rom 12:20 But if one who has hate for you is in need of food or of drink, give it to him, for in so doing you will put coals of fire on his head.
Rom 12:21 Do not let evil overcome you, but overcome evil by good.