If the citations say that the four major denominations are orthodox, reform, etc etc then it is OK with me to say "the four major denominations", and in a footnote say what those dnoms are.   this is the intro so we want to make it fairly breif.   you are correct, there is a problem with the "nearly all".   there is also a problem with "all"  the 200,000 messianic jews might consider themselves a major denomination.
further down in the article the statement that "all major jewish organizations (religious and secular) are opposed to j4j" is unacceptable, because there is no defined list of what the organizations are....the israeli national soccer team hasn't made any statement about j4j, so how can we assume they are opposed to j4j?