This verse, again, starts out like 6:12. Paul chooses a slightly different tack though. Where the previous verse focuses on me and my freedom, 10:23 looks at others. The goal here is the building up of others. Simply put, Paul says there are some things that pass the tests of lawful, worthwhile, and not enslaving, but he still avoids out of deference of others.
Jesus said that the definition of a true disciple is that the person loves others. Paul defines that love here by requiring us to build one another. Essentially, it not only has to be worthwhile for mu, but build others as well.
Joe Aldrich warns that this principle can be abused though. He calls these abusing people professional weaker brothers. They piously look down their nose at certain activities and claim that the activity offends them and, therefore, sinful for everyone. They lay this down as a trump card (maybe that is an unfortunate description) that ends the conversation and disallows any other opinions. Paul expects us to walk the line between drawing a true weaker brother into actual sin and standing against a pharisaical professional.
Both sides are very important to keep in consideration. Our participation will quite possibly change based on situation, people around us, and what God is teaching us at a particular time. This tension caused one young man quite a few years ago to respond, “I don’t want to think, just tell me what to do.” Unfortunately, Paul requires us to think.