Has there ever been a systematic persecution of Buddhist heretics?

I think the post of @Saptha Visuddhi is related to the question because it is very difficult to avoid this departure into why Buddhism became extinct in India when asked a question about heresy.

Generally, 'true believers' do not persecute others & it is the 'true heretics' that persecute others.

I would speculate King Asoka was related to the distortion of the teachings that gave pre-eminence to creating populist reincarnation & Brahmanism-directed (conversion) teachings, which ultimately lead to the extinction of Buddhism in India.

I would speculate Buddhism was a victim of its own anti-Brahmanism-directed propaganda.

If we read the Pali suttas, what became to be 'Hinduism' (eg. Tri-Murti of Brahma-Vishnu-Shiva or moksha after reincarnations) did not exist during the Buddha's life but, in fact, was possibly distorted adaptations of the Buddhist teachings.

For example, the Pali suttas contain suttas (MN 1, AN 4.124, etc) that equate each meditation jhana with a Brahmanistic god but then state attachment to being a Brahmanistic god leads to hell.

While such suttas appear to be a form of anti-Brahmanistic propaganda (not spoken by the Buddha), most Buddhists believe the Brahman cosmology to be a true & real Buddhist cosmology.

This shows how Buddhism was possibly a victim of its own anti-Brahmanism-directed propaganda & shows how monks with the True Dhamma were probably treated as heretics (while monks with the false teachings that were indifferentiable from Hinduism got absorbed into Hinduism) .

One has to ask what heretical atmosphere prompted Nāgārjuna to compose so many treatises in an attempt to expound a pure & genuine Buddhist doctrine of emptiness & cause-&-effect?

For example, last century in Thailand, there was a young monk, who named himself Buddhadasa, who began publicly teaching supramundane Dhamma, which resulted in the Thai religious authorities (for a short time) accusing young Buddhadasa of 'heresy' & seeking to disrobe him.

He was opposed by conservative monks and laymen such as those from the Abhidhamma Foundation and Anan Senakhan who strongly disagreed with his interpretation of Buddhism to the point of accusing that Buddhadasa devalues Buddhism by explaining it simply and that tried to match the ultimate truth of Buddhism with the ideas of modern man. Buddhadasa was even accused of being a heretic and communist.

In his book he wrote the title "What is Paticcasamuppada" (1971) showing the distinction between what he considers the interpretation of Buddhist teaching using Hindu concepts and in the Buddhist sense. He is convinced that uncritical adherence to the Buddhaghosa orthodoxy has obscured a real encounter with the Buddha's dhamma. The criticism of Visuddhimagga implies that Buddhadasa goes against the belief and understanding of not only most Thai Buddhists but also Buddhists in general. Consequently, he is condemned by some groups of monks and laymen as an ungrateful and heretical person who destroys Buddhism. On the other hand, his book has became an important reference which most of Buddhist students have to take into consideration.

Buddhadasa's Movement: An Analysis of Its Origins, Development and Social Impact

There is a lot more to what @Uilium mentioned in the earlier post. It was the moguls that did most of the killing of Buddhist Monks, and the process of decline continued until Buddhism got fully wiped out in India by the end of the 12th century, when Somapura Mahavihara (in the present day Bangladesh) was set ablaze. In 1199 CE Odantapuri Mahavihara close to Nalanda was burnt down after killing all the monks. Buddha’s place of Enlightenment, Bodhgaya too was attacked. If only the Mughals and other Muslims of yesteryear, were not like the present day ISIS, we would be having a lot priceless idols, monuments, original scriptures of Asoka era that were there at Nalanda and elsewhere. Let me now tell you’ll in brief how it all happened from the time of King Asokha.

As @Uilium mentioned, the third council got underway to purify the monastic order of the bad monks. These other monks who used to practice ‘Buddhism’ according to their own interpretations rose up again. It was a death blow to those who practiced the true dhamma. Their first act was to translate the Dhamma into Sanskrit. They rejected attaining of the Margaphala. At the time only the Brahmins’ Veda was written in Veda and Sanskrit languages. Brahmins never felt that other religions will be a threat to their own since Veda as it was the only religious script written in Sanskrit. However, after the translation of the distorted scriptures into Sanskrit by the falsified monks who were thrown away from the third council, the Brahmins started to argue pointing out its content. In trying to defeat these Brahmins, these other monks built large universities like Nalanda with the aim of learning the Veda. The language used in these universities was Sanskrit. They tried to outdo the Brahmins. They tried to argue with the Brahmins. This is in contradiction to the Alagaddūpama Sutta, which states that “if anyone tries to learn my teachings to argue with others, then he will be destroyed like the man who tried to catch a snake by its tail.”

When the monks won an argument the monks got the king to make the Brahmins their servants in the Nalanda University. The monks were beheaded when Brahmins won their arguments. The Brahmins went for the kill, because of the change that these monks have made to the Brahmin society. An extremist Sothern Indian Brahmin called Sankarāchārya rose up to break the power of these monks. The Musālman invaded India at this time. The Brahmins got them to first destroy Buddhism, or at least what was left of it. This was how the Buddhism got wiped out from India.

King Asoka liked the Dhamma so much that he lavished the monks with robes, food and medicine...

This attracted many fake monks...

Monks were beheaded in an effort to find the imposters but that didn't work.

They started the third council to purify the monastic order by questioning monks to find out who knew the Dhamma and who held heretical views so they could expell the real imposters from the Sangha.