Looking at the answers from @JeromyAnglim and @Fizz, their answers give a general feel that it is acceptable to reference Psychology Today within questions, but what about answers?
To summarise what @JeromyAnglim and @Fizz points out, excluding questions simply because they are based on PT is too drastic. Psychology Today falls into the realm of non-peer reviewed online content and there is nothing wrong with referring to it.
My point I would add is that it shows prior research which we require, and as @JeromyAnglim points out:
this site is a bridge between science and what the wider public find interesting. So in that sense, Psych Today might bring up a topic that the wider public finds interesting, and that perhaps we can provide a more scientific answer to.
I agree with these points when seeing a question using Psychology Today as a reference, but I have trouble accepting answers purely based on Psychology Today articles.
For the majority of cases, I have seen that Psychology Today articles contain no citations and references to corroborating studies they say exist.
This to me is unacceptable. We have a strict policy that all answers should be backed up with reliable references so that the answer can be independently verified, regardless of the reader's/answerer's background. How can anyone safely judge a non-referenced Psychology Today article as reliable?
The author may have a PhD or similar, but it doesn't stop that author claiming a study proves something when it doesn't, in order to imply they are justified in making an invalid statement. So in this sense I agree with @BryanKrause
This is where citations and references come into play. As an example, in the answer to Saying things to shock others, as pointed out by @Fizz in the comments
honestly that PT page sounds like bollocks. The ref it cites for "Excessive attention seeking is not a character flaw. It is a brain wiring response to early developmental trauma caused by neglect." is https://www.ncbi.nlm.nih.gov/pubmed/10831470 which I have no idea how someone can interpret like that; it's a study of trauma in adulthood etc.
In this case, the Psychology Today article is a very rare example which is cited and referenced, yet the referenced article does not actually prove their claim, making their article questionable.
How many other questionable articles are there in Psychology Today? Well that is open to debate and we cannot reliably answer that, but in my view, if an answer is given purely based on an uncited and unreferenced Psychology Today article, I would suggest to the answerer that they try and find a more reliable source for their claims as these articles cannot be relied upon to be correct and accurate.
If the Psychology Today article does contain citations and references, then I would hesitantly allow it but would not necessarily trust the "corroborating article" until I had chance to study it for accuracy.