To love one another with righteousness, means to love everybody with respect, in deed and in truth.
All text taken from the version of the King James Bible
I John 3:18 - My little children, let us not love in word, neither in tongue; (or, speech) but in deed and in truth.
I John 3:7 - Little children, let no man deceive you: he that doeth righteousness is righteous, even as he is righteouss.
I John 2:29 - If ye know that he (Jesus) is righteous, ye know that every one that doeth righteousness is born of him. (or, abides in Jesus and keeps the commandments.)
I John 2:1 - My little children, these things write I (John) unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:
I John 3:4 - Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law.
I John 2:3-4 - And hereby we do know that we know him (Jesus Chirst) if we keep his commandments. (4) He that saith, I know him, and keepeth not his commandments, is a liar, and the truth is not in him. See - Ten Commandments
I John 3:9-11 - Whosoever is born of God doth not commit sin; for his seed remaineth in him: and he cannot sin, because he is born of God. (10) In this the children of God are manifest, and the children of the devil: whosoever doeth not righteousness is not of God, neither he that loveth not his brother (11) For this is the message that ye heard from the beginning, that ye should love one another
This does not mean that you live with somebody and/or have relations with another person,---this would be called iniquity, wickedness or fornication -- See - Iniquity and Vanity; also Temples of God--Churches
I John 3:12 - Not as Cain, who was of that wicked one, and slew his brother. And wherefore slew he him? Because his own works were evil, and his brother's righteous.
I John3:14-15 - We know that we have passed from death unto life, because we love the brethren. He that loveth not his brother abideth in death (15) Whosoever hateth his bother is a murderer: and ye know that no murder hath eternal life abiding in him.
Rev. 21:7-8 - He that overcometh shall inherit all things; and I will be his God, and he shall be my son. (8) But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death. - See - Judgment, The First Resurrection and the Second Death
I John 3:20-24 - For if our heart condemn us, God is greater than our heart, and knoweth all things. (21) Beloved, if our hearts condemn us not, then we have confidence toward God. (22) And whatsoever we ask, we receive of him, because we keep his commandments, and we do those things which are pleasing in his sight. (23) And this is his (God's) commandment, That we should believe on the name of his Son Jesus Christ, and love one another, as he gave us commandment. (24) And he that keepeth his commandments dwelleth in him, and he in him. And hereby we know that he abideth in us, by the Spirit which he hath given us.
I John 4:7-9 - Beloved, let us love one another: for love is God; and every one loveth is born of God and knoweth God. (8) He that loveth not knoweth not God; for God is love. (9) Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins.
John 3:16 - For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
I John 4:11-12 - Beloved, if God so loved us, we ought also to love one another. (12) No man hath seen God at any time. If we love one another, God dwelleth in us, and his love is perfected in us.
I John 4:15-18 - Whosoever shall confess that Jesus is the Son of God, God dwelleth in him, and he in God. (16) And we have known and believed the love that God hath to us. God is love; and he that dwelleth in love dwelleth in God, and God in him. (17) Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world. (18) There is no fear in love; but perfect love casteth out fear: because fear hath torment. He that feareth is not made perfect in love.
I John 4:20-21 - If a man say, I love God, and hateth his brother, he is a liar: for he that loveth not his brother whom he hath see, how can he love God whom he hath not seen? (21) And this commandment have we from him, That he who loveth God love his brother also.
I Peter 1:22 - Seeing ye have purified your souls in obeying the truth through the Spirit unto unfeigned love of the brethren, see that ye love one another with a pure heart fervently: See -Iniquity and Vanity