The image above is making the following argument:
Premise 1: Things that look the same should be treated equally
Premise 2: Under the skin, we all _look_ the same
Conclusion: Therefore we should disregard all of the categories above and treat each other as equals.
The first problem is that its not true that we are all the same under the skin. There are numerous differences between us even in our skeletons. These differences are such that archeologists will still know a lot about us even when we are dead and gone.
Next, there are a number of problems with both premises. And a lot of it has to do with disregarding what the categories above are based on.
For example, black and white are two categories that deal primarily with skin. Therefore its invalid to show a picture of a skeleton in order to prove that no difference exists between blacks and white. Martin Luther Jr didn’t base his argument that he and his people should be treated equally on that argument. Instead he based his argument on the Bible which teaches us that we are all equal by virtue of our relationship to our creator. Not because we all “look” the same under the skin.
Then there is the issue with comparing one set of categories with another. For example, the black and white categories can be considered two elements of one set that we can express as (black, white). The next set of categories is gay and straight as those both deal with sexual orientation. That can be expressed as (gay, straight). And the final set, just for completeness, is (religious, atheist) which is based on acknowledgement of the supernatural or not.
Comparing the three sets of categories based on what the author supposes is a good argument for the equality of the first category (that we are all equal under the skin based on the general fact that we have bones) isn’t valid. Even if it were true that elements of the (black, white) set could be shown to be equal by the “everyone’s equal under the skin” function, it doesn’t follow that we can apply that same function to the other sets.
For example, we can’t say that the categories of gay and straight are equal simply because the have equivocal bone structure. That would be like saying that Mother Teresa and Hitler were really the same (ie equal) because they both had feet and hands.
The biggest difference between Mother Teresa and Hitler isn’t primarily physical. So a comparison based on a physical measure isn’t going to help us come to a correct conclusion about the relationship between these two people or elements.
Likewise, the difference between the sets above are not primarily physical so it follows that the image is wrong in its premise that things which look the same are the same since physical appearance is not the distinguishing characteristic of any of the categories above.