That's the entire point of the post and the earlier posts it links to.
But, yes, in general for libc, if the manpage didn't say it's thread-safe, it is unsafe.
Time, date, physical spellings, ... many things are locale dependant, but socket stuff?.
It comes as a Surprise!!, and not the good kind, to many a network programmer with just a few years under their belt to discover threaded networking can segfault because of this.
Once you know, you know and don't forget (until next time), but I suspect this was the motivation behind the blog posting, the principal of potentially most surprise.