I think questions like this are always going to be arguable because the depend on agreement on what makes a foreign word "part of the English language". What is the test? That it is in (say) the Oxford English Dictionary or Merriam-Webster? Most, if not all, of these words are.
Another test might be: are the words used by the general English-speaking public in ways other than to refer solely to the the original foreign concept or object? For example, "cafe" is certainly part of the English language, to the extent that the original é is optional, and because it is used to refer to any coffee house, not just those in France, or even in a French style.
I can't see this being the case with hijab and certainly not hajj. But what about fatwa? I think there might be an argument for that since English-speakers have started to use it rhetorically to mean a "death sentence" or other severe ruling other than those issued under sharia (I understand that a fatwa is not necessarily, or even usually, severe, but that is often how it is perceived).