Yeah, singular 'they' is one of my favorite fallbacks. I've also found that it is the least offensive (or most accepted) misuse of pronouns by those who are genderfluid, regardless as to whether or not you know their preferred pronouns, in that the speaker is consciously making an effort to include as many options as possible.

The only downside I've seen to using 'they' is that hard grammar cops will say that it's wrong to use a pronoun that is accepted as plural for singular use. These are the same people who will argue the literal usage of each word instead of its intent, though, and generally I wouldn't worry about them.

They is also used colloquially, verbally and in writing, in the US. It's not going to jump out at most readers, even those who aren't exposed or accustomed to the idea of genderfluidity.