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Is anti-Brahminism a characteristic of Asuras and Rakshasas?

Which group of created beings is the most anti-Brahmin (hatred and opposition to Brahminism and Brahminical way of life)?

Is anti-Brahminism characteristic of Asuras and Rakshasas?

Yes, the Asuras, Rakshasas, and Pisachas frequently engage in the genocide and massacre of Brahmanas and Rishis who live on Earth.

This section of the Vana Parva of the Mahabharata talks about how a particular clan of Danavas, called the Kalakeyas, wanted to destroyed the universe and genocide and kill all Brahmanas:

Demons' plan to annihilate the universe:

And struck with panic at sight of the assembled celestial host, the afflicted Danavas fled to the depths of the sea. And having entered the fathomless deep, teeming with fishes and crocodiles, the Danavas assembled together and began to proudly conspire for the destruction of the three worlds. And some amongst them that were wise in inferences suggested courses of action, each according to his judgment. In course of time, however, the dreadful resolution arrived at those conspiring sons of Diti, was that they should, first of all, compass the destruction of all persons possessed of knowledge and ascetic virtue. The worlds are all supported by asceticism. Therefore, they said, 'Lose no time for the destruction of asceticism. Compass ye without delay the destruction of those on earth that are possessed of ascetic virtues, that are conversant with duties and the ways of morality, and that have a knowledge of Brahma; for when these are destroyed, the universe itself will be destroyed.' And all the Danavas, having arrived at this resolution for the destruction of the universe, became highly glad. And thenceforth they made the ocean--that abode of Varuna--with billows high as hills, their fort, from which to make their sallies.

Documented genocide of Brahmanas:

"Lomasa said, 'The Kalakeyas then having recourse to that receptacle of waters, which is the abode of Varuna, began their operations for the destruction of the universe. And during the darkness of the night those angry Daityas began to devour the Munis they found in woody retreats and sacred spots. And those wicked wretches devoured in the asylum of Vasishtha, Brahmanas to the number of a hundred and eighty, besides nine other ascetics. And, proceeding to the asylum of Chyavana that was inhabited by many Brahmacharis, they devoured a century of Brahmanas that lived upon fruit and roots alone. And they began to do all this during the darkness of the night, while they entered the depths of the sea by day. And they slew a full score of Brahmanas of subdued souls and leading a Brahmacharya mode of life and living upon air and water alone, in the retreat of Bharadwaja. And it was thus that those Danavas the Kalakeyas, intoxicated with prowess of arms and their lives nearly run out, gradually invaded all the asylums of the Rishis during the darkness of the night, slaughtering numerous Brahmanas.

Consequence:

And every morning people saw the dead bodies of Munis emaciated with frugal diet, lying on the ground. And many of those bodies were without flesh and without blood, without marrow, without entrails, and with limbs separated from one another. And here and there lay on the ground heaps of bones like masses of conch shells. And the earth was scattered over with the (sacrificial) contents of broken jars and shattered ladles for pouring libations of clarified butter and with the sacred fires kept with care by the ascetics.

So, one can say for certain that anti-Brahminism is a quality of extremely evil Asuras and Rakshasas.