Is your choice of word-processing program an issue? Yes, it is, as you will see.
That said, arguably, this shouldn’t be an issue that only attracts attention now, at the start of typesetting. Normally, your editor (or her staff) should have had her fingers all over your text file(s), especially if it is the press undertaking the editorial work. Even if the deal is that you are supposed to deliver ‘clean’ text ready for typesetting, your production editor should have been on the ball and checked your files.
No? Oh well, at least in terms of word processor, it is likely that no harm has been done – because, let’s face it, the vast majority of authors use Microsoft Word (meaning there shouldn’t be a problem in this respect).
To some scholars, of course, Microsoft is the evil empire and they wouldn’t touch Word even if Bill Gates offered them a space suit and the use of an over-length barge pole. Nor is it necessary as such to write your text as Word documents; there are very good word-processing alternatives available (not least WordPerfect, Nisus Writer and – a fast-growing open-source rival – OpenOffice Writer).
Whichever software you use, it need not be Word but it must be compatible with Word – this is what your publisher’s editorial staff are likely to be using; they have to be able to open (and maybe change) your text files. In other words, your text files must be able to be opened in Word.
The same restriction is likely to apply for the typesetting. For instance, Adobe InDesign only imports text in .doc, .docx, .rtf and .txt formats. This means that if you have written your book in (say) WordPerfect, Nisus Writer or OpenOffice Writer, then – in order for it to be imported into the typesetter’s book file(s) – you will have to save your text as a Word or RTF file (not as plain text; you could lose any italics and other character formatting with a .txt conversion).
No, this may not be fair. But for now, like it or not, Word remains the 20-tonne gorilla in the playground.