I guess an Anti-Barney fan made that quote in order to have parents not let their kids watch the show.
On topic with the "Cookie Monster is allergic to peanut butter cookies" thing, I looked it up, and it appears that you got this info from Wikipedia. Well, I have something to tell you about that: Wikipedia isn't a reliable source. For example, on Disney DVD pages, some people will put something saying that Song Of The South will be coming out on DVD and Blu-ray "next year", the Furby page said that the 2005 movie "Furby Island" aired on The Hub in 2012 when it only aired on Nickelodeon and NickToons in 2005 and 2006, and on the Garfield and Friends page, someone said it aired on NickToons in the United Kingdom from 2008 through 2009, when only Nickelodeon's main channel aired the program in the late 90's in the United States and the United Kingdom. In fact, my eighth grade Social Studies teacher was against using Wikipedia due to unreliable info on there, such as "Hitler loved the circus".