Can you give an example of something relevant here which does not have a moral component?

There is something to your point regardless, but moral disparities do not proportionately account for the disparities here. The situations are more complicated. The political types of topics which seem to suffer here are laden with some impurity with considering. Many cultural and moral values shift like the wind, so why do political concerns seem so immutable? I think we would be fools to accept this as simply a moral disparity. I encourage considering a more complex model of social relations. The more significant influences at play here are symbolism, identity and politics.

Are there any rights that do not have a moral component?

The right to not be a slave is a moral right. That's literally the definition of a right. First entry from Google's dictionary:

> morally good, justified, or acceptable.

Morality can change and is changing, sometimes faster than law. Differences in morality shouldn't be insurmountable obstacle to introducing solutions that work for other generally otherwise similar parts of humanity.