Is a Front-End Web Developer a “Programmer”?
Is it accurate to classify web designers as programmers? Should they be classified as such?
No, web designers aren't necessarily programmers. Web developers on the other hand, designers or not, are arguably (and usually) programmers, irrefutably so if they use any server-side language or a scripting language.
Well it depends. If the web designer is strictly a designer, working within Photoshop, than they are not a programmer.
If they code their designs in HTML & CSS, I'd still say they aren't a programmer or even a web developer.
If they can write PHP and code their designs in HTML + CSS, I'd say they are a programmer, but not necessarily a web developer (Depends on their understanding of various other topics related to programming).