What do you call someone who hates pictures?

An iconoclast is, in its literal sense, someone who breaks images. The word derives from Greek εἰκών eikōn ‘image’ (also ‘shape’, ‘form’) and the verb κλάω klaō ‘break’ and literally means an image breaker.

As you’ve noted, though, the word is very heavily religiously laden, and moreover it’s mostly used in an extended, figurative sense, referring to someone who challenges (especially religious) views and principles.

There is a more appropriate formation also based on εἰκών, with the more familiar -phobe suffix, namely an iconophobe.

This is hardly a common word, but it is used. Wikipedia has an article on it, which describes it thus in its opening lines:

Iconophobia (literally fear of icons) refers to an aversion to images, especially religious icons. Iconophobia is differentiated from iconoclasm in that iconophobia refers to the aversion to or hatred of the images whereas iconoclasm refers to the actual destruction of images that may arise from iconophobia.

This is still a word with close ties to religion and religious philosophy. If you are going to use it in a written piece, you would be well-advised to specify if you’re using it in a non-religious context to refer to someone who just dislikes images in general.