It is only in writing that it really shows up, though.
I regularly talk to students about how they should deal with their tutors, and how they should consider who is the author of the bookk they are reading (this, in study skill classes), As both authors and tutors come in any possible variety of genders, I regularly refer to he-or-she, him-or-her-, his-or-hers in my lectures and never see any adversxe reaction from my audience (and this is often in groups as small as six or eight, where body-language feedback is very apparent.)

However, I do agree that in written language, it is obtrusive, if so written. As shona says, a little thought will permit you to write these things in reasonably smooth English, most of the time.