JOEL - I have never heard of young women being told by Church leaders not to join the Girl Scouts. As far as I know there have never been any formal statements from the church regarding individual participation in Girl Scouts. In fact I have known a few active LDS girls who were Girls Scouts. I had to buy cookies from them every year :-) There are many LDS Girl Scout leaders. LaRae Orullian was the first LDS member to be elected as President of the Girl Scouts Organization for the US in 1991and is now vice chairman on the World Board for the World Association of Girl Guides and Girl Scouts. So as you can see we are well represented in the orgaization.
However, I am sure the Church leaders believe that the LDS Young Womens organization, with the Peronal Progress program, offers a much better resource for development of character and testimony. The Young Women program has four main goals: (1) to help each girl become personally converted to the gospel of Jesus Christ, (2) to help her fulfill her divine potential as a daughter of God, (3) to help her gain an understanding of the priesthood and live worthy of its blessings, (4) to help her enjoy in wholesome ways her youthful vitality.
I can't see how the Girl Scouts program would help with any of these, except perhaps for goal #4. Perhaps one issue that prevents the church from fully embracing Girl Scouts, involves the somewhat liberal attitude of today's Girl Scout organization compared to the more conservative Boy Scouts. For example, the term "morally straight" found in the Boy Scout oath is not found in the Girl Scout oath. The Girl Scout organization does not reject known homosexual women as scout leaders; the Boy Scouts do. Religious values and beliefs are supported in the Girl Scouts, but including the words "to serve God" in their pledge as well as reference to any religious beliefs was recently made optional "to encourage diversity". The Boy Scout membership form states, "The Boy Scouts of America maintain that no member can grow into the best kind of citizen without recognizing his obligation to God."
For the most part these things probably have little effect on an LDS Girl Scout. The problem is, that in order for the Church to be formally involved at all with the Girl Scouts, it would have to accept and support it 100% as part of the Young Womens program, so that it could have some control on what the girls do in the organization. This is not likely to happen since the Girl Scouts would not give up control over who are put in as girl scout leaders in the local troups. The Church would also perhaps need to exert some influence against the liberal attitude of the existing Girl Scout organization, at least so far as LDS involvement is concerned. This would be very difficult and would be perceived as a "politically incorrect" thing to try to do. I guess the bottom line is that we simply don't need it enough to make it worth the effort.