In Seven Psychopaths (2012), a magazines (maybe a newspaper) publishes an audition for Seven Psychopaths in a classified section.
Do newspapers/magazines publish this type of ads in it?
Newspapers sell classified ad space for many varied reasons including Casting Calls etc.
They will have terms of service saying what should and shouldn't be included like these at the L.A. Times
As long as the advert isn't asking/selling anything illegal then they're free to print pretty much anything.
Take for example this one by Sean Penn
Now, granted this was published in South Africa and not the US (where there are specific laws regarding child actors) but the point is clear.
In the case of the linked image you provided, it's not even a casting call, it's a request for information...the psychopaths' stories for inclusion in a screenplay.
It might be more common for this to be published in a "trade" paper / magazine but generally, sure, if the advertiser is willing to pay, the newspaper will print it....especially at a premium rate for color! :)