I am wondering if it is true that...most of the slaves transported were Muslim?

No. It's a little bit hard to say exactly what proportion of all slaves that crossed the Atlantic were Muslim. Sylviane Diouf has offered the following cautious (and vague) statement about numbers^1:

To be sure, there were Hundreds of thousands of Muslims in the Americas, and for the time being, that may be all we can say about numbers and estimates.

on the other hand, Allan D Austin provides firmer numbers in his estimate, but speaks more narrowly about the territory that would become the United States.

Let us then boldly presume that 10% of West Africans sent to America from 1711-1808 were, to some degree, Muslim. This is something less than Park's and Rahaman's percentages of Muslims on slaves ships bound for America and something greater than that found by our narrators from the Gulf of Guinea. For the area presently comprising the United States we may begin with Higgins' import figure of 360,000 (four times Charleston's 90,000), may reduce it by 50% for captives coming from areas beyond Muslim intrusions (reflecting our earlier arithmetic, which yields a figure of 180,000, of which according to our presumption of 10%, 18,000 may have been Muslims for the Colonial era 1711-75.

Now, this estimate by Austin contains judgement calls on what the "correct number" of total slaves imported was, a rough estimate of how many would have come from regions of Africa beyond the scope of Islamic influence (for example, the large scale importation of slaves from Angola and Congo). And of course, Austin is starting off in 1711, and not including earliest periods of importation from founding of Virginia and Plymouth colonies onwards.

I've done some cursory searches, and it is hard to find good estimates for proportions of Muslim slaves going to Spanish, Portuguese, Dutch and French holdings in the new world.

However, some assumptions that Austin makes still hold true for the larger picture of the Atlantic Slave Trade. For instance, the Angola and Congo region supplied some 40% of all slaves transported to the New world. As already mentioned, Islam had not reached this region before the 19th century, so we should not expect any slaves from that region to be Muslim.

Of the remaining ~55% of slaves which originated from West Africa (plus the remaining 5% coming from East Africa) were coming from a cultural context where Islam was present, but was not necessarily the majority religion. Certainly there were regions like Senegambia were Fulbe, Tukolor and Wolof captives were much more likely to be Muslims. Additionally, there are documented instances like the case of Bahia province in Brazil where large numbers of Muslim Yoruba slaves were brought in between 1800-1835.

However, it has to be acknowledged that there were other communities like Bamana, Igbo, Fanti, et al who continued to practice traditional religion and had not converted to Islam.

I'd be interested in knowing your source for the 20-30% figure. As I have said, I'm having a hard time getting hard estimates for all of the Americas for the entire era of the trade. However, statements like this one by Paul Lovejoy^3:

With the increased demand of the Atlantic trade, people came not only from the interior of Senegambia but also from the areas to the north of the Bights of Benin and Biafra. These slaves are often identifiable in modern research because they were Muslims....Muslims and other slaves form the interior became particularly noticeable on the trade registers of the late eighteenth century, although they appear to account for only a relatively small proportion of the total number of departures from Africa for the Americas.

imply to me that Muslim slaves in the Eighteenth century (the height of the trade) would not approach that 20-30% figure.

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1 Servants of Allah by Sylviane A Diouf. pp 70.

2 from African Muslims in Antebellum America: a Sourcebook by Allan D Austin p.35. Quoted in "Created Equal: Slavery and Americas Muslim Heritage" by Race Capet in CrossCurrents vol 60, no 4 (2010) pp 551. http://www.jstor.org/stable/24462381

3 Transformations in Slavery by Paul Lovejoy, chapter 3 "The Export Trade in Slaves 1600-1800" pp 60. Here Lovejoy is in turn drawing upon data from Phillip D Curtin's work from *The Atlantic Slave Trade: A Census" specifically tabulations of the ethnicity of slaves exported from Gulf of Biafra and Gulf of Benin on pages 202, and 254-255