Not for me, but it would be for certain churches.
But I'm with the other Father Heathen ... because no LGBQT in their right mind would want to work for such a group, the question becomes moot.
Out of the ~4,800 taxpayer-funded schools in my province, about 1,500 are Catholic.
Full-time teaching jobs are hard to get. It certainly limits a person's opportunity if a third of the teaching jobs are off-limits to them.
And while they're waiting for that full-time spot, it's a lot easier for a young teacher to get by if they're on the supply list for both of the school boards in their area.
... so in this case, saying that LGBTQ people should just not work for an organization that disapproves of them effectively amounts to saying that LGBTQ people need not become teachers unless they have some other source of income to sustain them for potentially a long time.