I think that a spoiler tag is the most practical suggestion to address this issue, specifically (given site features that currently exist), but we may want to discourage meme-like images in answers. We can also have standards for how memes are posted that support broader stack goals.
Posting memes on the internet is a pretty ingrained practice, though some people are more attached to it than others. I agree with scohe001 in that this is probably not a fight worth picking overall, in terms of disallowing or requiring forced resizing of meme images.
My bigger concerns lie around how we want to handle the information memes convey, because the text in the images will generally not be searchable. If the meme itself is meant to express information vital to the answer in a concise way (which they generally are), then the information most crucial to answers will become invisible to future searchers. This will make it harder for future users to find questions and answers when searching the internet, and will also make it more difficult for regular IPS users to find specific, previous answers.
I suggest three things for how we want to handle meme postings in answers:
1.The meme must contain information directly relevant to the answer.
"Fun" memes, or images which are otherwise not necessary to the
answer, should probably be discouraged (if not outright prohibited).
2.Meme text, or the meaning/implications/conclusions from the meme text, should be typed out in the answer (just as if it were meme-less). This is strictly an indexing-and-searchability concern for me.
3.Meme images should be hidden by some means or other, by default. I, personally, don't have a strong personal reaction to them but as this site is used by many professionals in professional settings during the workday a profusion of meme images being visible by default is not ideal. Spoiler tags are, I believe, the best current feature to hide memes by default while still allowing users to post them. But I have no particular attachment to that specific approach-- my advocacy extends only as far as my preference for spoiler blocks over meme images on IPS.
The first of these three suggestions could be made a site rule, and we already enforce some standards (if informally) on unnecessary information in posts. The second two might be covered well by entries in the FAQ, and are things that any IPS member with editing privileges could add to a post without causing much of a fuss (since all of the information originally added to the answer will still be there).