Poconos, someone can play with the words of the petition, but ultimately it means jack, since you'd instead have to tamper with the words contained in the US Constitution, which would require a Constitutional amendment.
The UN can't do jack about the internal practices of countries like the US and UK, and the UN charter document contains aspirational goals, ideals that are nice to dream of, but the UN is quite toothless to actually enforce their aspirational statement. It's a pipe-dream, a "wouldn't it be great if" kind of thing.
As Simon said, the law firm involved is likely using it as a means to reach out to prospective clients who actually have an existing cause of action on which to file, based on an alleged violation of State or Federal law (much like the Conti case in civil court which alleges the WT failed to protect children from known pedophiles). It's good someone with a legal background changed the wording to make it less of an embarrassment, but that doesn't change the fact pattern of the basic environment, as I said in my opening words. Consider the petition as an advertisement for Zelkin law firm, but it's really no more than that, an inexpensive PR effort for some law firm to advertise their services to potential plaintiffs.
So sign the petition if you want to vent, but realize that it's not likely going to accomplish anything; with or without that petition, nothing is going to change within your or my lifetimes (or even within the your grandchildren's lives), esp when 75% of Americans are religious and believe in God(s). The move towards allowing the gov't to meddle into religious practices is going to be protested and fought by ALL organized religions (which have very deep coffers), but also by any citizens (which BTW includes atheist communitie such as the Atheist Community of Austin, one of their agendas being to insure a separation of church and state continues) who actually understand the advantage of keeping religion and gov't as separate entities, AS LONG as all applicable laws are respected.
Adam