I probably have about as much experience with the Boy Scouts as anyone my age can have. I have been continuosly registered since 1992 (Cub Scouts before that), am an Eagle Scout, and have worked 6 summers at Boy Scout camp (3 at local level, 3 at Philmont).
Boy Scouts is completely compatible with Catholic morality, and is excellent for the formation of any young male. As mentioned, as an organization the Boy Scouts are unwilling to give in to modern moral relativism. They continue to hold fast to their moral standards, even when this has cost them money and required expensive court battles. For example, the Boy Scouts continues to regard homosexuality (I presume activity, not just orientation) as incompatible with the Scout oath and morality, despite the loss of funding and meeting venues that this has caused in places. (punished by anti-“discrimination” policies) With respect to religion, while the organization does not distinguish between religions, reverence to a higher power is one point of the Scout Law.
This brings up an important point regarding religion. The Boy Scouts, while encouraging religious development, does not advocate any particular religion. This must be distinguished from indiffentism; the Boy Scouts does not make any claims or ever teach that all religions are equal, it merely makes no judgements of the truth of various religions. Instead, it teaches that people must be treated with respect, regardless of their religion, and affirms that reverence is a necessary part of being an upright person. The determination of which religion is true is left up to the individual.
As a Scout, a boy may occaissionally be exposed to interfaith worship. Summer camps will often have a chapel service at least one night, as may camporees, etc. Frequently grace is said before meals. There is nothing incompatible with Catholic theology in this… in fact, these services are generally planned to be compatible with all religions. As an example, the standard Philmont grace is:
“For food, for rainment, for life, for opportunity, for friendship and fellowship, we thank thee o Lord.”
As you can see, the theological content is intentionally minimal. Another example were the chapel services held at the council camp I worked at. Songs would be sung that while acknowledging and praising God, did not really define whose version of God. (think “America the Beautiful”) The closest it ever came to a specific religion was when the camp chaplain (in this case Jewish, pre-rabbinical) would speak. He would tell traditional Jewish stories about morality. However, these were basically a cross between parables and fairy tales, and never specifically Jewish in what they were suggesting, just in origin and style. However, I would consider carefully being a member of a troop that is all one faith except for you, as they might not make the same effort to have all services, etc. be interfaith. A troop that is mixed or of your religion, however, will be fine.
At the same time, while sometimes holding interfaith services, the Boy Scouts strongly advocates faithful adherence to ones own religion, whichever that may be, and never intends its services to supercede those of your own religion. Philmont (as a large enough camp) maintains Jewish, Protestant, LDS, and Catholic chapels and chaplains. (Mass is celebrated daily) (Islamic, Hindu, etc would probably also be offered if there were enough demand.) The prayerbook provided to Scouts at Philmont, in addition to containing an interfaith daily reflections, also contains ones for specific religions, and individuals and crews are free to use whichever one is compatible with them. (An all Jewish crew could use the Jewish prayer section. I personally found the Muslim section useful, though I was more interested in the sunrise and sunset table it contained than its religious content.)
Basically, the Boy Scouts does not distinguish between different religions, but encourages each Scout to faithfully follow his own religion. A Scout can earn a religious emblem (not required for any rank), with programs offered by most religions and administered by religious authorities of that religion. Additionally, Eagle, the highest rank requires three letters of recommendation: one from a school official, one from your parents, and one from your religious leader. So, Boy Scouts is quite compatible with Catholicism, and actually encourages a Catholic to be a good Catholic.
As to whether Scouts develop boys into the kind of men one would want ones sons to become… A significant fraction of the males that I know at my university that are actively involved, whether in the Knights of Columbus, as altar servers, or singing in the choir are Eagle Scouts, and still proud of the fact. The path to Eagle Scout develops character, leadership ability, and confidence.
