The trouble with Ayaan Hirsi Ali is that so many people take her seriously. The late Christopher Hitchens described her as "probably the most important public intellectual ever to come out of Africa" and last week it was the turn of a writer in the Wall Street Journal, no less, to hail her as "Islam's most eloquent apostate" and "the most dangerous foe of Islamist extremism in the western world".

This kind of hyperbole tends to accompany Hirsi Ali wherever she goes. She clearly knows a lot about PR, if not about Islam – which in the United States can be a definite advantage for a professional apostate. She is probably the only ex-Muslim that many Americans have heard of, though there are plenty of others – plus Muslim reformers – whose critiques of Islam are better-informed and more profound. Hirsi Ali's views, on the other hand, have the benefit of simplicity. They are not mentally taxing and can be easily digested, especially by the America's political right.

Her role as "a classic example of a persecuted dissident intellectual" (to quote American writer Paul Berman) has also tended to shelter her ideas from critical scrutiny; those who question them are liable to be accused of failing to show the support and admiration that she is thought to deserve.

In her 2006 book, Infidel, Hirsi Ali wrote: "I would like to be judged on the validity of my arguments, not as a victim", though her stated reluctance to be perceived as a victim is rarely borne out in practice. It's hard to find articles about Hirsi Ali that do not dwell on her victimhood and the Wall Street Journal's recent puff piece – by one of her colleagues at the Hoover Institution in California where she now works – emphasises that the writer met her in "a secure room" with a guard posted outside.

But, since she prefers to be judged by her arguments, let's consider her latest work, The Challenge of Dawa. This is not so much a book as a confused essay padded out to 105 pages – including advice for Donald Trump whose approach to political Islam she contrasts favourably with those of both Barack Obama and George W Bush.

As the title suggests, though, Hirsi Ali's main theme is a need to "confront" what she sees as the "threat" from da'wa. The ultimate goal of da'wa, she says, is "to destroy the political institutions of a free society and replace them with the rule of sharia law".

"In western countries," she continues, "dawa aims both to convert non-Muslims to political Islam and to instil Islamist views in existing Muslims." Da'wa is the organisational infrastructure that Islamists use "to inspire, indoctrinate, recruit, finance, and mobilise those Muslims whom they win over to their cause" – and "the new [Trump] administration urgently needs to devise an anti-dawa counterstrategy that employs the full range of tools at our disposal."

To the average American this will no doubt sound scary – and perhaps plausible. After all, as Hirsi Ali notes, da'wa is "a term unfamiliar to Americans". The average Muslim, on the other hand, is likely to find her description of da'wa baffling, if not laughable.

"Da'wa" comes from an Arabic verb meaning to call, summon or invite and, in a religious context, it's basically about proselytising. In Islam, calling non-believers to become Muslims or urging other Muslims to become better Muslims is seen as a virtuous activity, and several verses in the Qur'an recommend it:

Who is better in speech than one who calls to Allah, does righteous deeds and says indeed I am among the Muslims.(Qur'an, 41:33)

Let there arise among you a group inviting to all that is good, enjoining righteousness and forbidding evil. Those are the successful ones. (Qur'an, 3:104)

Call to the way of your Lord with wisdom and good preaching.(Qur'an, 16:125)

What da'wa actually involves is as varied as Islam itself. Of course there are some who spread hateful ideology and recruit jihadists under the guise of da'wa, and there are those whose "da'wa" would be better described as brainwashing. These are undeniable problems that can – and should – be addressed for what they are, not turned into an excuse for a generalised assault on the principle of da'wa. Contrary to the impression given by Hirsi Ali's essay, destroying the institutions of a free society is not what da'wa is actually about. 

Demonising da'wa – as a whole – because of abuses by Islamists is roughly equivalent to blaming "the internet" for offensive posts on Twitter. Hirsi Ali's eagerness to do so is also rather puzzling. Elsewhere in the essay she makes clear that Islam is not a monolith and that not all Muslims are Islamists but she seems unwilling to make a similar distinction with da'wa. It's almost as if she is trying promote "da'wa" as a frightening new Arabic buzzword to go along with "jihad", "sharia", etc.

Whatever the reason, characterising da'wa as a "threat" raises some major problems. First of all, she is de-legitimising what millions of Muslims (and, indeed, Christians) perceive as a worthy activity. Everyone, whether Muslim or not, has the right to proselytise. That is made clear in the freedom-of-speech and freedom-of-belief clauses in the Universal Declaration of Human Rights and also, for Americans, in the first amendment to the constitution.

A further problem arises when this is viewed in an international context. A crackdown on proselytising by Muslims in the west would play into the hands of Islamists and authoritarian regimes in Muslim countries where non-Muslims are already denied the right to proselytise. In other words, it would look very much like a game of tit for tat.

One might also argue that there's a need for more da'wa, of different kinds, rather than less – because extremist ideas flourish where they are allowed to go unchallenged. Hirsi Ali says she believes Islam can be reformed, and reformist da'wa by Muslim reformers would be one route towards achieving that.

In her essay, Hirsi Ali recognises that too little attention has been paid to forms of extremism that don't overtly support violence. Extremism – whether violent or not – does need to be tackled, and at an ideological level. But to say, as Hirsi Ali does, that da'wa "must therefore be countered as much as jihad" is too sweeping to be useful, and liable to be counter-productive.

Addressing the problem in a recent report for the UN Human Rights Council, Karima Bennoune, a law professor at the University of California, said the heart of both fundamentalism and extremism is that they reject equality and the universality of human rights. Fundamentalisms, in keeping with their theocratic visions, "impose their interpretation of religious doctrine on others as law or public policy, so as to consolidate social, economic and political power in a hegemonic and coercive manner". Quoting a previous UN report, she continued: "Fundamentalism is not simply about terrorism, extremism or even religion. It is, at bottom, a mindset based on intolerance of difference." 

Alluding to the struggle against apartheid in South Africa, Bennoune noted that extremists "will not be truly disarmed unless their ideology is comprehensively challenged and repudiated". This, she said, "explains why the United Nations did not simply focus on the abuses attendant on apartheid, but sought to dislodge the idea of racial superiority itself".

This analogy with South Africa and apartheid puts a clearer perspective on efforts to combat extremist ideology emanating from Islam. It is a global problem and tackling it on a purely national basis can never have more than limited success. The biggest obstacle to repudiating it is that the mindset of intolerance and denial of rights found among extremist groups has also been adopted and legitimised (and in some cases propagated) by governments in the Middle East – several of which are allies of the United States and supposedly partners in combating terrorism.