Horvat's article does a very good job of demonstrating that it is overwhelmingly likely that Washington did not convert to the Catholic faith on his deathbed, but the characterization of some of Washington's religious beliefs is not accurate. Washington believed in a personal God who acted in history through the agency of divine Providence. The Father of Our Country did not believe in a vague, impersonal deity.
While Washington, unfortunately in my view, did not convert to Catholicism (what a great story that would make!), he was a great advocate for the religious liberty of Catholics in the new Republic. As this post over at The American Catholic points out, Washington not only counted Catholics among his personal friends, but sought to protect the rights of Catholics to worship and participate in the life of the new nation: George Washington and Catholics.
Washington may not have become a Catholic, but Catholics in the United States owe him a tremendous debt of gratitude for preserving and defending their freedom to worship freely and live as full citizens of the United States of America.
Related item: here's a copy of the text of a letter George Washington sent to eminent Catholics in the young American Republic, upon his elevation of the office of the presidency:
While I now receive with much satisfaction your congratulations on my being called, by an unanimous vote, to the first station in my country; I cannot but duly notice your politeness in offering an apology for the unavoidable delay. As that delay has given you an opportunity of realizing, instead of anticipating, the benefits of the general government, you will do me the justice to believe, that your testimony of the increase of the public prosperity, enhances the pleasure which I should otherwise have experienced from your affectionate address.
I feel that my conduct, in war and in peace, has met with more general approbation than could reasonably have been expected and I find myself disposed to consider that fortunate circumstance, in a great degree, resulting from the able support and extraordinary candour of my fellow-citizens of all denominations.
The prospect of national prosperity now before us is truly animating, and ought to excite the exertions of all good men to establish and secure the happiness of their country, in the permanent duration of its freedom and independence. America, under the smiles of a Divine Providence, the protection of a good government, and the cultivation of manners, morals, and piety, cannot fail of attaining an uncommon degree of eminence, in literature, commerce, agriculture, improvements at home and respectability abroad.
As mankind become more liberal they will be more apt to allow that all those who conduct themselves as worthy members of the community are equally entitled to the protection of civil government. I hope ever to see America among the foremost nations in examples of justice and liberality. And I presume that your fellow-citizens will not forget the patriotic part which you took in the accomplishment of their Revolution, and the establishment of their government; or the important assistance which they received from a nation in which the Roman Catholic faith is professed.
I thank you, gentlemen, for your kind concern for me. While my life and my health shall continue, in whatever situation I may be, it shall be my constant endeavour to justify the favourable sentiments which you are pleased to express of my conduct. And may the members of your society in America, animated alone by the pure spirit of Christianity, and still conducting themselves as the faithful subjects of our free government, enjoy every temporal and spiritual felicity.