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Paul is no stranger to saying things that puzzle and perplex, and in Romans 14:14 the apostle once again says something that befuddles us: "I know and am convinced in the Lord Jesus that nothing is unclean in itself; but to him who thinks anything to be unclean, to him it is unclean" (NASB). Did you know that nothing is unclean in itself? Have you seen this truth in or through the Lord Jesus?
When we get clarity on what exactly Paul is talking about, we will find that we, too, know this truth through Jesus. In the Old Testament, the categories of "clean/unclean" were applied to food, temple or sacrifice objects, and what I call "conditions of living." The first two situations are pretty easy to grasp: you can eat this or you can't eat that, and this object can be used in the sanctuary service and that object cannot be used in the sanctuary service.
Human conditions could be a little trickier: if a woman was on her period or had given birth, if a man had a wet dream, if a home was found to have mold, if a person had a certain skin issue - all of these conditions of living could make someone "unclean" for a while, before the proper sacrifice, washing, and time allotment had transpired.
From the context of Paul's remark in Romans 14, it's very clear he's talking about food. Paul has been talking about issues in what you eat and how that impacts your relationships with others (cf. verses 2-6), and his reference in verse 13 to not judge each other is probably a continuation of his advice in verse 10 to not judge each other over food and observing certain feast days. But Paul is saying in Romans 14:14 that Jesus has shown him nothing in-and-of-itself falls into the "unclean" category. When he references things not being innately unclean, Paul isn't saying you can eat whatever you want - actually, Paul isn't concerned with what you eat or don't eat in Romans. Instead, Paul is saying it is clear that things can be declared unclean, but God didn't make anything - or anyone! - unclean at the beginning or in the present.
Friends, Jesus' incarnation testifies that God doesn't make junk or unclean things, whether animals or people. God invites you to accept the fact that you are always acceptable to him.