You're absolutely right. And as such, they should get no tax funding or privileged use of public facilities.
I could go along with that on a federal level, but only if taxes and the government were reduced to levels allowed for by the constitution. If the government were just a minor player in our lives that ran the court system, minted our money and guarded our borders against invasion then tax funding and public facilities for the Boy Scouts would not be an issue. When the government is involved in virtually every aspect of our lives however, saying that an organization must exist completely outside of it is discriminatory in itself. If you're going to cut off funding for the Boy Scouts for religious reasons, then by the same logic you should cut off medicare and medicaid in Catholic hospitals, AA, military chaplains, student loans, the GI bill and probably half of all other government programs.
By that logic, there should also be no taxpayer support for gay groups, womens groups, and no taxpayer support for things like "historically black colleges".
Why does this subject bother you so?
What a strawman. I can't think of one organization that is not, in some way or another, discriminatory.