This is where the "Separation of Church and State" comes into play. If the camp is wholly owned by the Lutheran Church (not a privately owned camp) they are under no obligation to acknowledge or accept homosexuality. They have every right to prohibit the attendance of openly gay persons and to require their staff to sign contracts including clauses supporting a biblical stance on sexuality.
Even the Boy Scouts of America won numerous lawsuits over the years pertaining to gay leadership and members before the organisation folded to liberal pressure.
Unfortunately in recent years there have been several denominations (including the Evangelical Lutheran Church in America) that have changed their policies to be more "inclusive". Specifically, the ELCA changed their policies in 2009 to allow for openly gay clergy and the "consecration" of homosexual marriage.
This is what I was going to point out. There are some very different branches of Lutherans around. Missouri Synod would never allow this. The ELCA would be delighted. I worked in Lutheran long term care run by both organizations. The ELCA would push "world" religions, the Missouri Synod paid for the Christian chaplains, got various churches to come in for monthly or weekly services, and made sure there was a general service every Sunday morning. There was no catering to gays, but that was 2013, maybe things have changed now?
I know the American Christian psychologists I am taking my PhD with say that the law is such that, if someone comes to you wanting to become gay, you have to help them, even as a Christian, employed by a Christian organization. On the other hand, if someone is gay and wants to change to straight, you can be arrested and put in jail for counseling that person, WHO WANTS TO CHANGE, from becoming straight.
I sincerely worry we have lost the battle in North America. The gays have just taken over. At Sunday's pride parade in Toronto, billed as "family friendly" with lots of little kids, lots of the gay men were walking around naked, with police standing there ignoring that it is indecent exposure, in front of little kids. I saw a photo of it. On the same day, a block away, a preacher had a Bible under his arm, and he was arrested. My country is done for! I had hoped if we got a Conservative government in, things might change, but now I fear that too many economic conservatives have walked away from the principles of social conservatism.
Oh, in Canada, if you are running a camp or some other useful summer service, you can get government funding to employ summer students. Except if you are Christian. The organization has to sign a statement agreeing that abortion is all right, or they will not get funding. A values test rigged against Christians. This was supposed to have been taken out of the summer jobs program after so many protested last year. Instead, Trudeau brought it back, on some level, and they have rejected many Christian summer camps.