I don't believe that this meme called anyone a snowflake. It didn't even take a position on the issue. It just pointed out that the headline is stupid. One year olds cry hysterically for any innocuous reason, that is not news headline worthy.
My guess is that you're so wrapped in you position on the issue that you can't see anything even loosely related to it through a non-political lens.
Not about the meme, but about your comment, empathy is over rated. It causes people to stop thinking logically and about risks and consequences of what they do (or don't do). It is how many murderers and rapists lure in their victims.

I said nothing about Mexico sending drug dealers and rapists or taking jobs. I don't even think anybody in this thread has.
The only mention even made of rapists was in regards to empathy, not immigration. I even clearly indicated that the comment was a response not to the main meme, but to the comment about empathy. Empathy is often touted as a supreme virtue. But if you allow it to over rule your logic, you will make stupid, and sometimes dangerous decisions.