This passage is sometimes taken to mean the commandments of God are no longer applicable for Christians. Here’s all of 1 Corinthians 6:12 and 10:23 so you can get a sense of that perspective.

“”All things are lawful for me,” but not all things are helpful. “All things are lawful for me,” but I will not be dominated by anything.” (1 Corinthians 6:12)

“All things are lawful,” but not all things are helpful. “All things are lawful,” but not all things build up.” (1 Corinthians 10:23)

If Paul was saying all things prohibited by God’s law are now lawful, he would be contradicting his argument in this passage. Only two verses prior, Paul lists acts that are unrighteous. (Unrighteous = lawless according to Romans 6:19 and 2 Corinthians 6:14.)

“Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality, nor thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers will inherit the kingdom of God.”  (1 Corinthians 6:9-10)

It would not support Paul’s argument to say idolatry, adultery and theft are unrighteous (unlawful) but then immediately flip and declare “all things” (including idolatry, adultery and theft) are lawful. There is another explanation that doesn’t create a contradiction.

Notice that verses 12-20 are in the context of rebuking the Corinthians for participating in prostitution. Also notice that some translations put “All things are lawful for me,” in quotations. In these verses, Paul is putting forth an anticipated objection on behalf of opponents and then refuting their argument. A paraphrase to convey the meaning might go like this: “Someone may argue, “Prostitution is legal under Roman law.” To that, I say not everything acceptable to Rome is beneficial for one whose body is joined to the Lord.”

Here’s what Dr. Craig Keener says in his commentary.

“Having listed various vices, including sexual sins, Paul now counters objections and establishes his case against immoral behavior to which some members of the church appear to be succumbing. In contrast to philosophers who denigrated or ignored the body, Paul emphasizes the body’s sanctity, with an argument that climaxes in the exhortation to “glorify God in your body”. The body, including its sexuality, was a divine gift to be used responsibly. Their new identity in Christ must shape their behavior (6:11, 13–17, 19–20). Paul deftly employs the language of ancient ethics to answer objections in 6:12–14. Philosophers and orators regularly employed criteria such as “lawful” and “profitable” for ethical decisions. Moralists often employed an interactive style in which they posed objections from an imaginary interlocutor; sometimes (as in 15:12; Rom 9:19; 11:19) they explicitly noted the interlocutor, but at other times (as here or Rom 3:1–9) they simply offered and refuted the objection (e.g., Cicero Scaur. 9.18;18.41). The NRSV rightly identifies the objections in quotation marks; whether or not some Corinthians had actually used these phrases (cf. 1:12; 7:1), the thoughts the phrases embodied represented the Corinthians’ best (potential?) objections. Simply because an action was “lawful” (literally, one’s “right,” perhaps meaning not illegal under Roman law) did not make it good for a person (6:12; also 10:23).”