No. There is a disagreement among the early authorities as to whether the Tallit needs to be white or not. The Rambam and Rashi write that the strings of the Tallit must be the same color as the Tallit itself. Tosfot, on the other hand, write that there is no obligation to do so and that the color of the strings does not have to be the same as that of the Tallit. Jewish Law follows the opinion of Tosfot.
