Regarding that image of the "tolerant liberal," it's personally baffling to me how some people see accusations of Islamophobia, homophobia, sexism, etc. as a matter of "not agreeing" with people. It's rarely that simple. My devoutly Christian great-aunt, since the federal recognition of same-sex marriages, and her support of Kim Davis' bewilderingly unfounded crusade, has claimed the Antichrist is going to appear on this world with a same-sex partner. Now, I'm going to go ahead and call that homophobic. I also don't agree with her, but my reason for calling that homophobic isn't because I don't agree. It's because it's literally grouping me and a whole community of people who have experienced everything from poorly-executed characterization in media to legally recognized trans panic defenses and hate-motivated murder, as inherently evil.
There are things that I agree are mostly simply a matter of "not agreeing", such as what to do with gun control. There are certain concerns regarding the "good gun-carryer", such as the concern of how often a black citizen legally carrying a gun will be afforded the same freedoms as white shoppers in Target. But intersecting topics aside, that's a topic I don't mind weighing in on.
However, a Muslim registry, as promoted by certain people of certain repute, is Islamophobic and racist because it promotes inherent suspicion/distrust of a group of people, and it would only be a matter of time before it came down to merely what one looked like (as if we'd have to wait for Islamophobic attacks on purported Muslims; post-9/11 was a particularly hard time for brown-skinned folks in general.)
And this particular image entertains the idea that all of these particular issues are the same, by belittling the anger expressed by people who are affected directly by matters that mean so little to the average American that the majority can only see it as "opinions." As a result, it's surprisingly common to find people who are so expecting of me to justify my existence, or why I should have the privilege of equal rights, because for them, who I am is little more than something to debate.