I'm not sure what scholars this article is referring to, but it sounds like a deliberate misrepresentation of the decline of Islam in 15th and 16th century Iberia (or Al-Andalus as the Muslim-ruled portion of the peninsula is sometimes called). That being said, there is a grain of truth to the claim. After the forced conversion of the Muslims of the former Muslim state of Granada in 1500-1502, Christian authorities did show a particular concern with regulating the way these former Muslims dressed.

First and foremost though, let's clearly establish that Islam declined in Iberia because of the active persecution of Muslims by the Spanish monarchy. To give a quick overview, the Christian kingdom of Castile conquered the last remaining Muslim state in Iberia, the Emirate of Granada, in 1492. The capitulation stipulated that the Muslim population of Granada would not be forcibly converted to Christianity. However, as Christian rule continued, tensions grew which led to a rebellion in 1500. This provided the Christian rulers with the justification to rescind the provisions of the 1492 and force all the Muslims of Granada to convert to Christianity, or else emigrate out of Castile (something they also made difficult, forcing them to travel overland out of the kingdom rather than the much easier passage by boat to North Africa). By 1502 then, the open practice of Islam was eradicated in Castile (the forcible conversion of the Muslims of the other Spanish kingdom of Aragon would follow in 1526). This more than anything else spelled the doom of Islam in Andalusia.

Obviously these forced conversions did not make Christians out of the Muslims of Granada overnight. Christian authorities were well aware that such forced conversions were not particularly sincere, but they believed that over time they could truly win these former Muslims over. There was some debate over how exactly to do this, but basically the church leadership adopted both a carrot and stick approach. On the one hand, they sought to convince the former Muslims of Christianity through sermons and education. They established new schools and regularly preached in Muslim-dominated areas. At first they even translated Christian texts into Arabic. On the other hand, they worried about the pull of traditional Islamic practices and how they could foster an attachment to the population's former faith. As a result, over the course of the sixteenth century local authorities and the Spanish monarchy promulgated numerous bans on “Moorish” practices. Some of these had a clear religious connection - a 1511 proclamation stipulated that former Muslims must get their meat from a Christian-style butcher to ensure that they were not adhering to halal standards.

The boundary between a religious and a cultural practice is a porous one however and sometimes Christian authorities targeted practices which were not explicitly religious, but basically seemed “Moorish.” Here we get to the issue of veils. The same 1511 proclamation mentioned above also stipulated that former-Muslims were to dress like Christians. We have to be careful though about making too many assumptions here: in the sixteenth century it was common for both Muslim and Christian women to cover their hair. Women in Granada wore a distinctive enveloping outerwrap called an almalafa. Here’s a link to a 16th-century drawing of the veil to give you some idea of what it looked like. Christian authorities associated this article of clothing with Islam, but moreso because of its style than it's purpose as a veil. In fact, in 1513 Queen Juana of Castile made a proclamation banning Christian women from wearing the almalafa. The Queen notes that “Old Christian'' women have adopted the wearing of the almalafa, ignoring the instructions that “the newly converted should leave aside their Moorish dress and clothing.” She chides them for setting a poor example and mandates that if caught the clothing should be confiscated and they be given 100 “strokes of the whip.” The fact that this proclamation was re-issued ten years later suggests that the Christian authorities continued to see the adoption of “Moorish” clothes as a hindrance to the process of conversion of the Muslim population.

So, the grain of truth behind the statement in the article you read is that clothing was an important part of the religious and cultural identity of early-modern Muslim Iberians and that Christian authorities targeted Granadans dress in an effort to clamp down on Islamic practices. But, the decline of Islam in Andalusia was instead the result of a program of forced conversion and persecution of which restrictions on dress were only a part.