The WTS didn't become "involved" with the UN, not in any shape, form, or fashion. The WTS merely became a "member," remember?
Here is something I got from quotes.jehovaswitnesses.com. Its part of a relolutiom p;edged by all the assemblies in 1963.
WE JEHOVAH'S witnesses, met together in [City, State, Country], in one of the "Everlasting Good News" assemblies being held in a continuous chain around the whole world this year of 1963, do this day declare and resolve as follows:
5 THAT, in order to prevent the destruction of the nations by their own means in war, the nations further refused the surrender of their sovereignty to God's Messianic kingdom by setting up a society of nations, which, since 1945, has taken the form and the name of the United Nations, with international headquarters at New York city. This international organization stands for world sovereignty by political men. For years men without faith in God's kingdom have endeavored to get all people to worship this international image of human political sovereignty as the best hope for earthly peace and security, in fact, the last hope for humanity. To date 111 nations have given worship to this political image by becoming members of it. However, we, as witnesses of the Sovereign God Jehovah, will continue refusing to engage in such idolatrous worship, for we see, under angelic enlightenment, that God has smitten such idolaters with a malignant ulcer, symbolically speaking, that will spell death to them as spiritually diseased image worshipers who worship a man-made political creation rather than the Creator of heaven and earth;
How do you explain this?