You would have that impression if you only quote Romans 6:11, but if you continue reading verses 12-16, Paul explains exactly what alive in Christ means—
that we are to be servants to righteousness, not sin.
Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord. Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. For sin shall not have dominion over you: for ye are not under the law, but under grace. What then? shall we sin, because we are not under the law, but under grace? God forbid. Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness? —Romans 6:11-16
Here are numerous verses that equate righteousness with commandment keeping. Even Romans 6:16, which I'll repeat again.
Know ye not, that to whom ye yield yourselves servants to obey, his servants ye are to whom ye obey; whether of sin unto death, or of obedience unto righteousness? —Romans 6:16
And it shall be our righteousness, if we observe to do all these commandments before the Lord our God, as he hath commanded us. —Deuteronomy 6:25
My tongue shall speak of thy word: for all thy commandments are righteousness. —Psalms 119:172
O that thou hadst hearkened to my commandments! then had thy peace been as a river, and thy righteousness as the waves of the sea. —Isaiah 48:18
And they were both righteous before God, walking in all the commandments and ordinances of the Lord blameless. —Luke 1:6
For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them. —2 Peter 2:21
Which brings us back to the OP. If we receive knowledge, that righteousness includes commandment keeping, but we do not obey God's holy commandments, we are sinning willfully.
Concerning love as fulfillment of the law (because I know that's what's going to come up next):
Paul said that love is fulfillment of the law (Romans 13:10). If you stop there, like you did when you quoted one verse (Romans 6:11), you only get an abstract of what Paul means when he says love. If you pluck the verse (Romans 13:10) and ignore the commandments of God, you are ignoring the very meaning of love. This doesn't negate Romans 6, it expands upon it, just as Jesus did (Matthew 22:36-40), when He pointed to old testament scripture (Deuteronomy 6:5, Leviticus 19:18) and quoted words that He Himself gave Moses on Mt. Sinai. Jesus hung the law and the prophets on love, forever tying love to the commandments of God and scripture itself. Therefore you can't say love is fulfillment of the law if you are not keeping the commandments of God
and not reading scripture in full context.
Context is key. Romans 13:
Let every soul be subject unto the higher powers. For there is no power but of God: the powers that be are ordained of God. Whosoever therefore resisteth the power, resisteth the ordinance of God: and they that resist shall receive to themselves damnation. —Romans 13:1-2
Let us walk honestly, as in the day; not in rioting and drunkenness, not in chambering and wantonness, not in strife and envying. But put ye on the Lord Jesus Christ, and make not provision for the flesh, to fulfil the lusts thereof. —Romans 13:13-14
Jesus warned against adding or taking away
(Revelation 22:18-19). Picking and choosing scripture is troublesome, because it removes context and replaces it with abstract ideas that aren't scriptural—
which is willful sin on multiple levels
. The refusal to accept the truth found in scripture is a
conscious choice. The refusal to accept the commandments of God as hanging on love (Matthew 22:36-40) is a
conscious choice.
In the face of overwhelming evidence to the contrary, there is no excuse.