It helps to remember that the term for worship in Romans 12:1 is latreia, which is defined as service. Furthermore, its Hebrew equivalent (aboda) was used in the Old Testament primarily to describe the acts of service associated with worship typically performed by the priests and Levites, such as offering sacrifices (cf. Josh. 22:27; 1 Chr. 28:13). Incidentally, the majority of the times latreia is used in the New Testament is contextually in descriptive references of these duties of the Old Testament priests (cf. Rom. 9:4; Heb. 9:1, 6)
One should also keep in mind that a major theme found repeatedly in the New Testament is how things in the Old Testament serve as a copy and foreshadowing of spiritual truths found in the New Testament (Heb. 8:5; 10:1; Col. 2:17; cf. Rom. 2:28; Col. 2:11-12; et al).
Let’s also take note of something else which is relevant. Latreia (service, worship) in Romans 12:1 is specified as spiritual in nature in the verse.
Thus, what Paul is doing in Romans 12:1 is making a comparison between the type of service offered by the Old Testament priests and the type of service offered by New Testament priests, who consist of all Christians (1 Pet. 2:9).
He’s basically saying, “Just as the Old Testament priests offered service to God through animal sacrifices, Christians must offer themselves as a living sacrifice, i.e., every aspect of their lives. The Old Testament priests offered physical sacrifices, and thus their service was physical in nature. Christians, the New Testament priests, by contrast offer their entire lives as spiritual sacrifices, and thus their service is spiritual in nature.”
So Romans 12:1 is not saying that our entire lives must be non-stop worship 24/7, as some believe and teach. Really stop and think about the implications of that teaching for a minute. If our entire lives are to be non-stop worship, then that would require that worshiping God would include the acts of sleeping, going to the bathroom, watching a baseball game, being physically intimate with our spouses, working at our secular jobs, driving home in rush-hour traffic while listening to a self-help audiobook, and yes, even giving into temptation and committing sin…as 1 John 1:8 makes clear that Christians do. That simply doesn’t make sense, and is not true.
Rather, Romans 12:1 is saying that our entire lives must be given up to serve God in every aspect of our lives. And when we fall short and sin, serving God requires us to acknowledge that we’ve sinned, repent, ask God for forgiveness, and continue serving him (1 John 1:7-9).