What everyone else has said. It didn't take me long to learn to type only one space (hey, it's less work), and now double spacing looks odd to me. I've also read that double spacing is more likely to create "white space rivers" in a document, which can be very distracting to people with certain visual or cognitive differences. This is a good reason not to use monospaced fonts as well, and not to right justify manuscripts (unless specifically requested to on submission guidelines, of course).
If you really can't help typing that extra space after a period, you can always use Word's search and replace function prior to submission, where you replace every double space with a single one (or, if you are converting your font to a monospace for some reason, you can take every period with one space after and convert it to a period with two spaces after).
I doubt there are very many people out there who will summarily reject an otherwise flawless manuscript if you double space after periods, but it's one of those "little things" that can put some readers off and possibly have an additive effect. I've read enough rants about its screaming that the submitting author is "old," and evidently being "old" is a bad thing to some people who consider manuscripts, resumes*, and letters of application, so...
*Though so does having attained one's terminal degree back in the 90s or earlier, and I don't know what one can do to hide that.
