I am not a native speaker of the English language, so I am probably incorrect about the use of their in this context.
Shouldn’t it be the last post (or his / her last post) instead of their post?
The following link suggests clearly that the word their is only used within a plural context.
Their, they, them, despite traditionally being a plural, has recently adopted a genderless singular usage, spawning specifically out of recent non-binary movements to account for individuals who do not feel either he, his, him or she, hers, her are appropriate or for whom a gender is not known.
The origins date before this, of course, but it has become much more popular to use they recently.
See also xe, xim, xer? Those spellings could be off, I’m not thoroughly versed this week, month, year’s favourite labelling
If you see ‘their’ used in this context, assume it is a politically correct substitute for his, her, or the like
To address specifically why “the last post” would not sound appropriate here, it is a little more subtle, but I think “the” is too strong of a word in this instance, and feels more appropriate to be in reference to the forum as a whole rather than the user’s specific activity.
To add to the foregoing, the gradual acceptance of “they” as an all-purpose neuter pronoun has been progressing for some 40 years. Ironically, it arose from a misunderstanding of the development of pronouns and of gender in English. See, for example, Early English by John W. Clark.
Okay, clear. Still feels a bit weird though.
How about the previous post?
This is also gender neutral and politically correct (the last being a fashionable term I am disgusted with; I just don’t like to feel a public pressure on what to think).
Correct to use this, though it comes across as more formal.
“Most recent” would be the most precise usage.
I think I remember reading that they for singular dates back even to the 18th century or so. I used to find it weird when it came up recently for non-binary people, but now, honestly, I don’t mind at all and it starts to feel natural and more easy on the eye than s/he or more exotic things.
I sympathize. “Politically correct” came from the Marxist lexicon, and its early use in the U.S. was usually sarcastic. Unfortunately, that is now lost, and it has become regularized in the language.
Cool that this topic started a linguistic discussion.
Same in the Netherlands.
The humourless have taken over and legitimised it.
But the next time I will hear someone say politically correct, I will ask them why they use a Marxist concept and if they (their, they’re?) sympathise with Marxism. 
Personally, I love the ‘they’. Wish we’d have something like that in German.
you probably do, it’s just probably 40 chars long like the rest of your words 
Only 40 characters?
In the context of the thread it doesn’t make sense, the previous post is the one before this one, their previous post is specifically saying that this person hasn’t posted anywhere on the forums in many months, not just something about the post preceding the message. As in the post, the one before the banner, could have been written five minutes ago. ‘The’ sounds too confusing in my opinion.
Anyway, I also like to use they, them, their, in particular on the forums because I don’t know whether to use him/her etc in most cases, but also because it doesn’t bother me to try using him/her. They/them works fine 
Sorry, just couldn’t resist posting this screenshot. 
And no, we don’t have to repeat the discussion above.
But, them?
I don’t like the term either. When I use “they” etc. as a singular pronoun, I’m not doing it for political reasons, I’m doing it because it feels most inclusive and welcoming to me. Calling it “politically correct” has the undertone that it’s actually incorrect, but we’re choosing to ignore that for a political reason.
The English are the strange ones here. Compounding nouns is the reason German is famous for its long words, but the same can be done in Dutch, and in the Scandinavian languages. English does it as well to a small extent (e.g. “football”), but only with short words.
Dutch has been suffering from people writing spaces in between their compound words, which we call the “English disease”. It’s probably mistake number 1 you’d find when checking texts for errors.
Using their and them in this context is normal “plain English” I would say. In a legal context you might need to use alternatives but this is a kind of everyday context and wording that is natural.
You definitely couldn’t use “the” . You could say “this forum user” but that would be so clunky. And I think it would be the same problem for any other formulation.
On the inclusive usage point, I’m not young and have used they/them as the singular in cases where gender is unknown all my life. It’s just normal English usage. The change is that it’s now suggested as a usage instead of gender assumptions. That doesn’t seem like a bad thing. Assumptions often need challenging.
Ugh, I hate it so much in German when people write stuff like Sommer Ferien or Büsten Halter.
Ich auch (me too).
But I’m afraid it’s something like “language economy” that would prevent it … in English “they speak” is even shorter than “she/he speaks” while in German “sie sprechen” is longer than “sie/er spricht”, and AFAIK there is a tendency in language to develop to the more economic side.
I wish it was like Japanese: no pronouns unless really necessary, and even then names / roles are preferred.
