The idea of inclusive language can be controversial, and different people have very different ideas about what is and isn’t inclusive, and it can all be terribly confusing sometimes … but like so much else in writing, it comes down to purpose and audience.
If you want your writing to reach as wide an audience as possible, you need to avoid language that unnecessarily excludes people. (If you do want to exclude some people, then of course you should use language that excludes them.) It isn’t really about your feelings — you might think, “Calling people with brown hair ‘Greenheads’ is a flattering term!”, but people with brown hair might find it odd at best, offensive at worst. What have you gained by using your term rather than a more open one?
Here’s a more realistic example: Some people really believe that “mankind” always has been and always will be a universal word that includes all homo sapiens. And it may in fact have been in the past read as universal — before the 1960s or 1970s, you can find countless examples of even staunchly feminist writers using “mankind” to mean everybody. But it doesn’t mean that anymore. That’s just a fact. Many many many readers will read the word “mankind” as sexist. Unless that’s a fight you want to put energy into, why not just use a more inclusive word like “humankind” or “people”?
I expect you will try to avoid obviously racist, sexist, heterosexist, etc. language in my class, because your peers (and I, your teacher) have various identities, and unless you really want to offend people, it’s generally better to try to be civil, open, and friendly. Obviously, it’s a judgment call, but that’s something we’re trying to refine: your judgment as a writer. The best and most flexible writers have the most sensitive ears for language and spend time thinking about the little distinctions that can matter a lot.
Don’t be afraid to use they/their as a singular pronoun, despite what any self-proclaimed grammarian tells you.
The singular they has a long history in English [see also this more recent link, regarding Taylor Swift], and I think it solves our language’s pronoun gender problem pretty nicely. Anybody who says they can’t be used as a singular is flat out wrong; it has been used that way for centuries. Feel free and encouraged to use it in my class.
Here’s an example. Instead of writing “Whatever his/her own feelings, a student is best off avoiding sexist language,” try replacing his/her with their. (His/her suggests there are only 2 genders. Using that construction leaves out people who don’t identify as male or female, and plenty of such people exist.) Our sentence rewritten with a singular they would read: “Whatever their own feelings, the student is best off avoiding sexist language.”
Of course, that sentence could easily be re-cast in the plural, and that’s the most elegant and least controversial solution: “Whatever their own feelings, students are best off avoiding sexist language.”
For thorough guidelines on using inclusionary rather than exclusionary gender language, see the National Council of Teachers of English website. (If your writing requires specific reference to transgender people, please be sure to be familiar with the terms in the GLAAD Media Reference Guide glossary.)
Really, this all can be boiled down to general advice about language: Use words purposefully and thoughtfully, and do your best to think about how your words could be read by someone who is not you. Purpose and audience.