Numbers 15:37-41 and Deuteronomy 22:12 tell us to wear tzitzit.
Why was this commanded and does the reasoning still apply? Let's look at the text.
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The LORD said to Moses, “Speak to the Israelites and tell them that throughout their generations they are to make tassels for the corners of their garments, and put a blue cord on the tassel at each corner. These will serve as tassels for you to look at, so that you may remember all the LORD’s commands and obey them and not become unfaithful by following your own heart and your own eyes. This way you will remember and obey all My commands and be holy to your God. I am Yehovah your God who brought you out of the land of Egypt to be your God; I am Yehovah your God.”
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Numbers 15:37-41
The reason provided here for tzitzit (tassels) is to remind oneself of one's allegiance to the Old Testament. This seems just as a valid today as it did at that time. So the reasoning does still apply.
But I would like suggest an additional reason for wearing tzitzit that isn't mentioned. The Old Testament repeatedly states that the Israelites are to be set apart from other nations. The idea here was to protect the Israelites from corruption from other nations. This was done mostly by chasing the other nations out of Israel. This approach no longer works, so we need another way of setting ourselves apart. I suggest that dressing differently, like wearing tzitzit, does set us apart.
The importance of dress and symbols cannot be underestimated. This gives people a sense of identity. This is why armies and other cohesive groups require a uniform. All strong religions have some form of distinctive dress. To develop a strong identity apart from modern culture, we should wear some distinctive symbol in public. Doing this requires real strength because most people feel uncomfortable when being seen as somehow strange in public. But once they dress distinctly in public, they will feel set apart from modern culture and will feel that their primary allegiance is to their religion.