By reading German newspapers (specifically taz) I became acquainted with the Binnen-I (enwiki, dewiki), where the letter I is capitalised in the middle of a word to indicate both male and female are included. For example: PolizistInnen, ArbeiterInnen, KollegInnen. Although Google Search is case insensitive and therefore useless, Google Ngram appears to indicate this usage started in the 1980s and has been rising steadily since then. Is it appropriate to use this politically correct spelling in a formal context, such as in a cover letter for a job application, or is this spelling mostly limited to the demographic of KreuzbergerInnen and other vegetarian cyclists?
This is an oddity of the taz newspaper, who made it somewhat popular among its readers. If you address the same audience, expect hate mail if you don't use it (or the alternative -in/innen or "Gendersternchen").
If you address any other audience and write like this, expect to be identified as "one of them". You will also receive hate mail occasionally.
My approach is talking to normal people in normal language and leave both sorts of idiots alone in their cages.
As you specifically asked about writing a cover letter for a job application, I don't see a problem at all. You as a person have one gender, not multiple. Your future employer should be able to address you properly, that is. So use distinct instead of indifferent language.