A gay couple, holding hands whilst walking in a park, might receive verbal abuse. As would, say, a transgender person. But an asexual person...well, I might have passed many whilst walking in a park. I would not have known they were asexual. 

Not saying abuse could NEVER happen, but the guy or woman in a bar/park/on a bus could be asexual. We'd likely never know.

A gay couple, holding hands whilst walking in a park, might receive verbal abuse. As would, say, a transgender person. But an asexual person...well, I might have passed many whilst walking in a park. I would not have known they were asexual. 

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Discrimination ≠ verbal abuse

The issues that asexuals deal with are akin to the issues that of atheists in the US, where they are, as Paul stated, looked at as "less than". The Gallup polls in recent years have consistently shown that the American public would more likely vote a Muslim President than an Atheist one, which is kinda impressive given the prevalent Islamophobia in the West. Similarly, there are studies showing that people have negative opinions of a person if all they are told is that person is asexual.

The other issues are visibility and erasure, in the same way that bisexuals have to deal with both straights and gays telling them that they are either straight people going through a phase or gay, asexuals have to deal with being told that they just haven't found the right sexual partner yet or that they just have sexual hang-up.

This does not equate to hate crimes, but this isn't equal treatment either.

Almost 100% of the time they receive surgery soon after birth so that they can easily be assigned male or female.

This can lead to serious psychological issues down the road.

It's always existed. It's a perfectly "legit" category.