Remember first that 'secular' in the Middle East is not the same thing as secularism in France or the United States. The separation of church and state, or of mosque and state, is rarely as solid as what we see in Western nations.

In one sense, Assad's Syria was doggedly secular. The Baath Party, which Assad led, was designed specifically to be a secular socialist party, in direct opposition to Islamist movements which sought to mix politics and religion. It was founded by a Syrian Christian, later led by Syrian Alawites, and open to members of all faiths. It was generally most strongly supported by religious minorities (as opposed to the Sunni majority), who felt that the alternative to Baathist secularism was Sunni dominance under an Islamist government.

The Baath Party's primary opposition was the Muslim Brotherhood, an Islamist organization which sought a greater role of religion (Sunni Islam) in politics. Assad outlawed the Brotherhood in the 1960's, and famously and bloodily decimated them in Hama in 1982.

But this secularism wasn't total. I'll quote from John McHugo's great book, "Syria: From the Great War to the Civil War":

Hafez al-Assad would have preferred a constitution for the country that was completely secular but, was prepared to compromise. The Muslim Brotherhood and other Islamist forces did not achieve their greater objective of cementing Islam as the religion of the state, but they were granted an article in the constitution providing that the president should be a Muslim. That was something Hafez al-Assad could easily live with.

Assad had a Shia imam declare a fatwah that Alawites were officially Muslims, and thus Assad would be complying with this article in the Constitution. He also did a number of other non-secular activities as president, such as going on a pilgrimage to Mecca, and creating a Koran-recitation prize (named after himself).

So even secular Baathist Haffez al-Assad was forced to water down his fairly militant secularism in order to placate a Sunni-majority country with strong Islamist impulses and fairly violent opposition groups. But this is typical in other 'secular' Middle Eastern states like Egypt and Turkey as well, in which the standards for what counts as secularism are much lower than you see in the West.