Perhaps you should mention which Fitzgerald person you are referring to.

To directly answer the question you asked, how widely accepted is Fitzgerald's claim, I think you will find that this is not his idea, but that he is rather part of a group of scholars in the field of Religious Studies who are seeking to problematize the historical definition of "religion" and make explicit the underlying assumptions present in the term. There are many others in the field that would mostly agree with his statements, key members being Russel McCutcheon, Tomoko Masuzawa, Brent Nongbri, Bruce Lincoln, Peter Brown, among many others.

I first want to challenge your simplification of Fitzgerald's claim. Religions were only "created" in the sense that their boundaries were carved out by a tacitly accepted or sui generis definition of what was inherently "religious" and those aspects are specifically modeled upon Protestant Christianity. A good place to start if you would like to see how this definition arose and what the implications of its usage are, see: Hans Kippenberg's "Discovering Religious History in the Modern Age" (although it suffers from a bit of an awkward English translation). Similarly, Tomoko Masuzawa's "The Invention of World Religions: Or, How European Universalism was Preserved in the Language of Pluralism" will provide another good example. Fitzgerald's contention with "religion" is probably better summed up from this blurb about his podcast on "The Religious Studies Project":

Fitzgerald presents his critical deconstruction of religion as a powerful discourse and its parasitic relation to ‘secular’ categories such as politics and economics. Religion is not a stand-alone category, he argues; ‘religions’ are modern inventions which are made to appear ubiquitous and, by being removed to a marginal, privatised domain, serve to mystify the supposed natural rationality of the secular state and capital. Feminist deconstruction of gender categories shows how power constructions which serve male interests come to appear as natural and inevitable, a powerful analogy to the mystification of power relations by the modern invention of religious and secular domains. (http://www.religiousstudiesproject.com/podcast/podcast-timothy-fitzgerald-on-religion-and-mystification/)

Here we can see that the issue with "religion" is that it doesn't play by the rules of a modern scientific taxonomy. Rather it defies rationalization of categories, and operates on a "you'll know it when you see it" kind of basis.

A great series of essays on this topic is Russel McCutcheon's "Critics Not Caretakers: Redescribing the Public Study of Religion." His arguement is that if we are to be public intellectuals, we cannot be caretakers of the religions we are studying. We can not accept "insider" arguments about what is actually occurring in any ritual or mythical practice, and be rigorously using a definition of "religion" that is clearly delineated and makes certain our audience knows what we mean and that the terms are being used with purpose. He also drops one of my favorite lines, which is:

As scholars of social authorizing practices, we fail to fulfill our role as public intellectuals when we decline to demonstrate consistently that such a thing as society, text, nation, ethnicity, tradition, intuition, gender, myth, or even religion, is “not a natural or god-given entity, but is a constructed, manufactured, even in some cases invented object, with a history of struggle and conquest behind it (140).

Finally, you can't leave a post about religious studies without citing J.Z. Smith, so I would recommend his "Imagining Religion" as he uses a wonderful array of different traditions to analyze the problematic nature with which the term "religion" is applied, and argues instead that we need a multi-thetic (multi-layer or many sided) definition of the term religion so that it is flexible or versatile enough to have meaningful significance to scholars. That being said, a counter argument could be that such a multi-thetic definition renders the word meaningless because it is too flexible, which brings us right back to those scholars demanding we do away with "religion" as a flawed category.

This is just a jumping off point, and reading these references will give you a clearer picture of the actual arguments against the term "religion" as a modern, Protestant concept, but will set you up well with a good theoretical basis for studying religion.

edit: formatting, still getting used to quoting