THEMSELF is getting more popular.

I think a lot of language purists dislike the word THEMSELF, even though language learners often see a logic in using it.

The usage over time is interesting, according to Google:

It spiked in the early 1800s before growing in popularity from the 1970s until now.

Even for non-language-purists, there is a right and a wrong way to use the word. We should use it in place of 'himself' or 'herself' when the gender is unclear. We shouldn't use it to replace 'themselves'.

Right:   A person who scores an 8.0 on the IELTS test may well feel proud of themself.
Wrong: They all did well on the IELTS test and they felt proud of themself. (should be themselves)