I suppose that there's a possible chance of that law passing in Ireland, where it's mainly the Catholic Church that runs its own school system. There will be Church opposition, but if the law passes, the Church will grudgingly adjust to it.
Such a law would have a much, much more difficult time in the U.S. Here, too, most of the religious schools are Catholic. A few years ago, a lesbian who coached at my own alma mater was terminated from her job when her marriage announcement ( to her partner) was published in the local newspaper. She accepted her termination gracefully, stating that she'd enjoyed the time she'd spent there, and wished them well in the future. Many of the students protested against her termination, and the other teachers had nothing but good things to say about her. I believe that she made an intentional effort not to seek out publicity about the matter, and she intentionally kept a low profile. She wasn't closeted during her employment, and most, if not all, of her co-workers knew about her being a lesbian. The school maintains a "Don't ask, Don't tell" policy, where gay employees are tolerated as long as they don't publicly announce their sexuality. If such a law went into effect in this country, I think the old, conventional Catholic schools wouldn't have much problem complying with it. The diocesan administrations would bitch about it, but the rank-and-file school administrations, I think, would actually welcome it.
However,a good many of the fundamentalist denominations run their own religious schools now, and they appear to be on the increase. For many of them, the whole raison d'etre for their existence is dissatisfaction with the public schools. They would be sure to scream bloody murder about any such law.