Here is what Chabad says concerning the reasons for not wearing the blue string...
http://www.chabad.org/library/article_cdo/aid/529771/jewish/Why-do-some-have-a-blue-string-in-their-tzitzit.htmWhy do some people have a blue string among their tzitzit fringes?By Menachem Posner
We read in the Torah:1 "Speak to the children of Israel and you shall say to them that they shall make for themselves fringes (tzitzit) on the corners of their garments, throughout their generations, and they shall affix a thread of techelet on the fringe of each corner."
The verse contains two commandments; one it to affix (white) fringes on the corners of a four-cornered garment, and the other is to add a thread of techelet to each corner. These two commandments are independent of each other. When techelet is available we are enjoined to add a techelet fringe to the tzitzit, and when unavailable we fulfill the mitzvah with plain white fringes.
Techelet is wool dyed with the blood extracted from a sea animal called the chilazon.
So why is it not so common today to have a techelet fringe on the tallit or tzitzit? At a certain point in history, approximately 1000 years ago, the chilazon, which was always hard to come by -- to the extent that the Talmud2 tells us that it only surfaced once every seventy years -- became unavailable altogether. After a while, its exact identity became unknown.
There have been many who have tried to rediscover the identity of the chilazon. Most notably among them were the Radziner Rebbe, Rabbi Gershon Henoch Leiner (1839-1891) and Israeli Chief Rabbi Y.I. Herzog (1889-1959).
Rabbi Leiner maintained that the cuttlefish was the lost chilazon and proceeded to produce and distribute dye produced from this fish.
Recently, the marine snail Murex Trunculus has been identified as possibly being the elusive chilazon, and many use its dye.
Most communities, however, view the findings of these groups as uncertain, and therefore continue to wear only white fringes, awaiting the coming of Moshiach when Elijah himself will guide us in uncovering the identity of the chilazon.
Yours truly,
Rabbi Menachem Posner