Based on this answer do tzitzit have to be white?
Where is the source that they should be?
I know that they are supposed to have at least one blue (techelet) string, but even that is disputed nowadays.
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The Gemara talks about "white strings" vs. techelet strings.
As I heard it from Rabbi Hershel Shachter mp3:
Rambam reads "white" as "matching the color of the garment." Thus, a pink garment would have pink strings (except for one techelet). The other Rishonim read "white" as "white" (or at least the natural color of the fiber, not sure you'd have to bleach it.)
While it's quite clear that the halacha here doesn't follow the Rambam, to avoid contradicting his view, we prefer a white garment -- hence, white strings according to everyone.
The Shulchan Aruch: Orach Chayim Siman 9:5 states the following:
י"א שצריך לעשו' הציצי' מצבע הטלית והמדקדקים נוהגים כן: הגה והאשכנזים אין נוהגים לעשות הציציות רק לבנים אף בבגדים צבועים ואין לשנות [ת"ה סימן מ"ו]:
Some say that it's necessary that the colour of the tzitzit and tallit are the same, and those who are particular are accustomed to practice this way. REMA: and Ashkenazim are accustomed to make only white tzitzit, even for coloured garments, and there is no need to change [the custom]
(Shared Previously by Double AA)
The lashon used by the Rema seems not to explicitly prohibit making colorful tzitzit. The question relies on the permissibility of changing a minhag.
A follow up question: In Mishneh Torah Tzitzis 2:8, The Rambam states:
טַלִּית שֶׁהִיא כֻּלָּהּ אֲדֻמָּה אוֹ יְרֻקָּה אוֹ מִשְּׁאָר צִבְעוֹנִין עוֹשֶׂה חוּטֵי לָבָן שֶׁלָּהּ כְּעֵין צִבְעָהּ. אִם יְרֻקָּה יְרֻקִּין אִם אֲדֻמ אֲדֻמִּין.
"If a garment is entirely red or green, or of any other color, the fringes which ordinarily are white should be of the same color as the garment; green, if it is green, red; if it is red."
What about a garment that is half red, and half green?