She can come off as somewhat racist (alienist?), but if you talk with her, it's actually more that she's mistrustful of other species in the same way one would be of agents from other countries that yours has a tentative alliance with. A sentiment exasserbated by her dads story.
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If you were a soldier on board the most advances ship in the US military and you commander allows an agent from the Russian military full access, I imagine you would be a bit concerned too.
The problem is Mass effect blurs the line between racism and nationalism. Every species is effectively a nation, and putting the human systems alliance first and not trusting the others, is then not racist, but can be mistaken as such.
On the citadel Ashley tells the xenophobic political candidate guy to stfu and she refuses to work with shep on Horizon because of shep's assosiation cerberus.
If you want racist, take a look at the Illusive Man.