Are there many journals that do not accept TeX/LaTeX?
The answer is that in some fields (La)TeX dominate whereas in other fields (La)TeX is largely unknown. Obviously any field where equations are required is more likely to be using (La)TeX for writing and publishing. However, it is not uncommon that journals, or rather, type-setters of journals, use LaTeX for final production regardless of submitted format. The same applies to book publishers. But, the fact is that the use varies and one needs to check with the journal to which you wish to submit.
The fact that you are not "allowed" to write your thesis with (la)TeX is perhaps because your advisor does not use it. I am an avid LaTeX user and am struggling to convince both colleagues and students in my department to at least try using it so I know how difficult it can be. In the end, I need to use both to be able to communicate with my colleagues and peers. So although I do not see why you should not set the thesis in (La)TeX in the end, you probably need to use word for the manuscript so that your advisor can provide input on files you supply. But, check how many journals actually use LaTeX in your field and strike up a discussion with your fellow students and your advisor. I think it is worthwhile to be fairly fluent in using many tools.
Edit: I will just add that I was convinced by a friend to use TeX (not LaTeX, it was a long time ago) when I wrote my thesis (a monograph at a US university) while almost no-one in the department used TeX; but then my advisor always provided feedback from double-spaced printouts which were platform independent. Those were the days.
There are many journals that do not accept, or actively discourage LaTeX-based submissions. I've always found the assumption in LaTeX heavy fields that it's ubiquitous to be an interesting quirk.
For example, two journals that will accept LaTeX based submissions, but would rather you not:
American Journal of Epidemiology:
Prepare your manuscript, including tables, using a word processing program and save it as a .doc, .rtf or .ps file. All files in these formats will be converted to .pdf format upon submission. Please note: This journal does not accept Microsoft Word 2007 documents at this time. Please use Word's "Save As" option to save your document as an older (.doc) file type.
On LaTeX:
Prepare any other files that are to be submitted for review, including any supplementary material. The permitted formats for these files are the same as for manuscripts and figures. Other file types, such as Microsoft Excel spreadsheets and Powerpoint presentations may be uploaded and will be converted to .pdf format. It is also possible to upload LaTeX files but these will not be automatically converted to .pdf format (and are therefore discouraged). The journal staff, editors and reviewers will only be able to view these unconverted files if they have the appropriate software, which cannot be guaranteed.
Epidemiology:
Manuscripts should be in a standard word processing format. We prefer Microsoft Word but we can also use RTF, TXT, LaTeX2e, and AMSTex. Application software programs released before 2001 are not supported.
The New England Journal of Medicine actively doesn't accept them, at least not unless converted to a PDF:
All text, references, figure legends, and tables should be in one double-spaced electronic document (preferably a Word Doc). You may either insert figures in the text file or upload your figures separately. We prefer the former, but this may not work well for complicated graphics, which should be sent separately. It is permissible to send low-resolution images for peer review, although we may ask for high-resolution files at a later stage.
Legends for all figures should be included in the file with the text and should not appear on the figures.
Our preferred file type for new manuscript submissions is a Word or text document with all figures in the same document. We will also accept Adobe Acrobat portable document format (.pdf) , WordPerfect (.wpd), text (.txt) documents, or .rtf file format.
Clinical Infectious Diseases doesn't even want your PDFs:
The preferred format for submitting manuscripts online is Microsoft Word (.doc files). PDF files are not acceptable for submission.
These are all very good journals in my field - a happy, healty, high-impact, tenure friendly career could very easily be had never touching LaTeX.
Yes, journals that do not accept LaTeX do exist. If LaTeX is not widely used in your field you might have surprises even with those journals that claim to accept it, since they in fact almost never have to. I recently submitted a manuscript in LaTeX to a Taylor & Francis journal which stated it did accept LaTeX submissions, only to find my piece "unsubmitted" the next day with a request to re-submit in Word.