(**Sources to be added.)
The problem of publicly-funded Protestant/Catholic schools was an outcome of the history of Canada. When the British defeated the French in 1763 Canada was populated with mostly RCs, but the official religion of the British Empire was Anglican (ie., non-Catholic). To avoid internal fighting the British govt gave the residents of British North America the right to organize RC Shools, but only if the same right was extended to Protestants.
This compromise was maintained as the provinces developed. When Canada was split between Upper (Ontario) and Lower (Quebec), the right to have two systems was maintained. In Quebec this protected the rights of Protestants (who didn’t want to be indoctrinated by Catholics.) In Ontario it protected the rights of Catholics (who didn’t want to be indoctrinated by Protestants.) This was an agreement reached by the leaders of the two main parts of the colony of Canada.
This was formalized further in 1867 at Confederation. Gradually the “Protestant” school system became secular – not run by churches, or including specific religious teaching or practices. Whereas the Cathoic system (also publicly funded) maintained its insistence on including religious training.
So to call the “public” system “Protestant” is a misnomer in today’s Ontario. It is a secular system open to all and with no overt religious content. The “right” to publicly funded religious schools is limited and, arguably, discriminatory. This “right” is not available to Muslims, Hindus, Buddhists, or any religious group other than Roman Catholics. It is completely the result of political compromises made since the founding of Canada.
In typically Canadian fashion we have never made a serious effort to “solve” this problem. As in the case of the use of our odd relationship to the British monarchy our usual response is “What’s the big deal?” Of course there is some wisdom in this approach. Being hard-headed about religious issues in politics usually ends up badly (e.g., Ireland). So perhaps it is best to just let this one fade away until no one takes religion seriously enough to care.