What should be a Buddhist's response to derogatory depictions of Buddhism?

Let's not forget that within Buddhism there is a healthy dose of self-deprecating humor and the occasional irreverence for depictions of the Buddha:

Tianran Roasting the Buddha, painting by Sengai Gibbon (1750-1837)

Danxia Tianran (739-824), a famous disciple of 8th-century Chan masters Mazu and Shitou, was spending a night at a ruined temple with a few traveling companions. It was fiercely cold and no firewood was to be found. Danxia went to the Buddha-shrine hall, took down the sacred wooden image of the Buddha, and set it ablaze to warm himself. Reproached by his friends for this act of sacrilege, he said: “I was only looking for the sharira (sacred relic) of the Buddha.” “How can you expect to find sharira in a piece of wood?” asked his fellow travelers. Replied Danxia, “Ah, well then, I am only burning a piece of wood after all. Shall we burn a few more?”

Story told by Ven. Ajahn Brahm, from this page, on how to respond to abuse, such as the destruction of Buddhist scriptures and statues:

There were riots in the streets some years ago after a guard at Guantanamo Bay was accused of taking a holy book and flushing it down the toilet.

The next day, I took a call from a local journalist who told me he was writing an article about the outrage by asking leaders of all the major religions in Australia the same question he was about to ask me.

“What would you do, Ajahn Brahm, if someone took a Buddhist holy book and flushed it down your toilet?”

Without hesitation I answered, “Sir, if someone took a Buddhist holy book and flushed it down my toilet, the first thing I would do is call a plumber!”

When the journalist finished laughing, he confided that that was the first sensible answer he had received.

Then I went further.

I explained that someone may blow up many statues of the Buddha, burn down Buddhist temples, or kill Buddhist monks and nuns; they may destroy all this, but I will never allow them to destroy Buddhism. You may flush a holy book down the toilet, but I will never let you flush forgiveness, peace, and compassion down the toilet.

The book is not the religion. Nor is the statue, the building, or the priest. These are only the “containers.”

What does the book teach us? What does the statue represent?

The Buddha himself was never disturbed by abusive speech hurled at him and taught that if abuse is not accepted and reacted to, then it stays with the abuser. The Buddha taught us to respond calmly and not be provoked into anger.

I have heard that on one occasion the Blessed One was staying near Rajagaha in the Bamboo Grove, the Squirrels' Sanctuary. Then the brahman Akkosaka Bharadvaja heard that a brahman of the Bharadvaja clan had gone forth from the home life into homelessness in the presence of the Blessed One. Angered & displeased, he went to the Blessed One and, on arrival, insulted & cursed him with rude, harsh words.

When this was said, the Blessed One said to him: "What do you think, brahman: Do friends & colleagues, relatives & kinsmen come to you as guests?"

"Yes, Master Gotama, sometimes friends & colleagues, relatives & kinsmen come to me as guests."

"And what do you think: Do you serve them with staple & non-staple foods & delicacies?"

"Yes, sometimes I serve them with staple & non-staple foods & delicacies."

"And if they don't accept them, to whom do those foods belong?"

"If they don't accept them, Master Gotama, those foods are all mine."

"In the same way, brahman, that with which you have insulted me, who is not insulting; that with which you have taunted me, who is not taunting; that with which you have berated me, who is not berating: that I don't accept from you. It's all yours, brahman. It's all yours.

"Whoever returns insult to one who is insulting, returns taunts to one who is taunting, returns a berating to one who is berating, is said to be eating together, sharing company, with that person. But I am neither eating together nor sharing your company, brahman. It's all yours. It's all yours."

"The king together with his court know this of Master Gotama — 'Gotama the contemplative is an arahant' — and yet still Master Gotama gets angry."

The Buddha:

Whence is there anger for one free from anger, tamed, living in tune — one released through right knowing, calmed & Such.

You make things worse when you flare up at someone who's angry. Whoever doesn't flare up at someone who's angry wins a battle hard to win.

You live for the good of both — your own, the other's — when, knowing the other's provoked, you mindfully grow calm.

When you work the cure of both — your own, the other's — those who think you a fool know nothing of Dhamma.

When this was said, the brahman Akkosaka Bharadvaja said to the Blessed One, "Magnificent, Master Gotama! Magnificent! Just as if he were to place upright what was overturned, to reveal what was hidden, to show the way to one who was lost, or to carry a lamp into the dark so that those with eyes could see forms, in the same way has Master Gotama — through many lines of reasoning — made the Dhamma clear.
SN 7.2

The Buddha taught:

50. Let none find fault with others; let none see the omissions and commissions of others. But let one see one's own acts, done and undone.

51. Like a beautiful flower full of color but without fragrance, even so, fruitless are the fair words of one who does not practice them.

Dhp 44-59