Islam and Judaism have some proscriptions for dress, in addition to certain traditional and cultural dress norms. For example Torah commands men to cover their head during prayer in reverence to God, the most well-known form of Jewish headdress that serves this purpose is the kippah, also called a yarmulke.
Christianity doesn't offer anything similar. Though it has been traditional to interpret 1 Corinthians 11 as men should have their heads uncovered while women have their heads covered (hence, the tradition of women wearing veils in church); though interpretation of this passage is diverse.
Clerical dress, varied by culture and tradition, is the closest thing to a distinguished Christian form of dress; though the purpose of clerical dress serves symbolic and liturgical purpose, and when not leading worship something such as the clerical collar in the West provides a way for people to recognize a pastor outside of the liturgical setting. What is worn and how it's worn is not a matter of Christian proscription but rather serves other purposes borne out of various traditions at different points in the history of the Christian Church.
I would argue that the Christian commandment to modesty would mean that we shouldn't be trying to stand out with our appearance. This in keeping with other things the Lord taught, for example when we fast we shouldn't go around saying we're fasting wearing sackloth and ashes in order to appear holy and spiritual to others. Likewise, the Lord teaches us not to engage in long elaborate prayers in public to draw attention to ourselves, but instead to quietly go inside a closet and pray. Of course I'm not suggesting public prayer is wrong, or that wearing ashes is wrong when fasting--but that the intent is to not draw attention to oneself; the focus isn't on us and our spiritual life shouldn't be flashy and involve showmanship. We are called to humility, quietness, and discipline.
I don't see any reason to wear special "Christian clothing" the very idea seems absurd to me. For one, because as already noted there's no such thing as "Christian clothing" (and, yes, I'm saying those really lame Christian t-shirts don't count as "Christian clothing"), and for another we aren't called to stand out. The Lord says we are a light on a hill, not because of the way we dress, what we listen to, or whatever--but by doing good works.
"In the same way, let your light shine before others, so that they may see your good works and give glory to your Father who is in heaven." - Matthew 5:16
-CryptoLutheran