Lubavitch is by no means modern orthodox. Modern othodox does not mean "modern", as in modern era, some modern orthodox are more "modern", but modern orthodox is a derech, or pathway/ philosophy, just like Chassidic, hareidi etc...
The KIPPAH to Wear or Not to Wear? Is it in the Torah? The Kippah origin comes from the Babylon religion where the pagan Babylonians covered their head when they prayed to their idols. While in Babylonian captivity some Jews copied the pagan Babylonians and covered their heads when they prayed to GOD. The wearing of the Kippah is actually Not in the Word of GOD. Throughout the Old Testament the Elect would take on the religious activities of other people. GOD would send a prophet to warn the Jewish people what would happen if they continued in other practices than what GOD said to do in the TORAH. The prophet also said what would happen if the Elect turned from your wicked ways to GOD, ask forgiveness that GOD would heal their lives and the land. Wearing a Kippah is being outside of the Torah and outside of walking with Elohim. The wearing of the Kippah is not from the Torah but comes from the writings of Sages and Rabbi.
For God so loved the world, that He gave His only begotten Son, that whoever believes in Him shall not perish, but have eternal life.``For God did not send the Son into the world to judge the world, but that the world might be saved through Him.``He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten Son of God.``This is the judgment, that the Light has come into the world, and men loved the darkness rather than the Light, for their deeds were evil.``For everyone who does evil hates the Light, and does not come to the Light for fear that his deeds will be exposed. `He who believes in the Son has eternal life; but he who does not obey the Son will not see life, but the wrath of God abides on him." The one who believes in the Son of God has the testimony in himself; the one who does not believe God has made Him a liar, because he has not believed in the testimony that God has given concerning His Son.And the testimony is this, that God has given us eternal life, and this life is in His Son.He who has the Son has the life; he who does not have the Son of God does not have the life.These things I have written to you who believe in the name of the Son of God, so that you may know that you have eternal life.