It's difficult to give a proper answer, because during any century of Middle Ages there could be many reasons for closing trading routes for European merchants as outsiders in various parts of Islamic world (which is huge). And it didn't need to have anything in common with religion - it could be the level of civilization (early medieval Europe), an economic matter in the particular case, or just a result of war.
But let's try to clarify few things.
First of all, Islamic world, in fact, wasn't that closed to Europeans as we think. Jews and Christians could live at Muslim lands if they paid special tax. The same with merchants from Europe. What's more, some Christians could even serve to Muslim rulers at important positions, such as revenue collectors or administrators of various types.
It's nicely described in the book "Daily Life In The Medieval Islamic World" by James E. Lindsay. You can find it's full text in the link, look for pages 120-121.
Also there's a good source for that in "Europe and the Islamic World: A History" by John Tolan, Henry Laurens and Gilles Veinstein, at pages 80-81. Unfortunately in both cases I'm not able to copy-paste it.
I believe that a bit about the overall history of the trade between Christians and Muslims during Middle Ages could help you solve the problem. I'll quote Jihoon Ko and his article "Economic Impact the Islamic World Had on Christian Europe (11th ~14th century)".
The conquest of Muslims of various regions of Europe had actually
ceased the major long-distance trade of the Christian Europeans
overseas for a while and the commerce of Christian Europe had been
limited to the local ones. But the regions which were under Islamic
rules were included in the commercial sphere of the Muslims—who were
the most active adventurers and entrepreneurs at the time—saw the rise
of international and complicated commercial activities. The
international trades in Christian regions were late to appear. The
crusade created a large influx of Eastern goods and luxuries into the
Christian Europe. This created a large interest among rich Europeans
for the Eastern goods, and the Christian merchants saw this to be an
opportunity for a dramatic profit. As the merchants began to actively
engage in the trade with the Islamic world, the trade of the Christian
states overseas began to flourish. The leading states of the trade
with the East were Italian city-states, most notably Genoa and Venice.
The extent of the international trades before the 11th century,
however, was nothing compared with those of the Muslim world. The case
of Al-Andalus indicates how well established was the Andalusi
merchants’ trades compared with the Europeans in the same era.
This way first, European (Christian) international trade wasn't well developed until 11th century, mainly due to the fall of ancient culture. It took European civilization a lot of time to get up after that.
But there were some smart merchants who made a fine business by initiating contacts between both worlds. They were, of course, Jews.
There were some global commercial activities going on in the Christian
world, however, before the Christians began to trade over long
distance, by the Jewish merchants. The Jews were also the first
merchants in the Middle Ages to introduce goods from the East to the
Christian Europeans. They supplied goods from the Islamic world as
soon as the Carolingian era. The Jews could travel to Europe with
relative ease. Some of them settled in Italy, but majority of them
were those who based their commerce in the Muslim countries. The Jews
from the Muslim world reached Western and Northern Europe through
Spain. At first, they exclusively traded spices, pepper, manufactured
goods, and other precious stuffs from Egypt, Syria, and Maghrib. They
provided the goods to the churches which used the goods to make
incense for religious activities, and to the selected nobility.
When European trade market became more international, the crusades started. One could imagine that it made the trade more difficult, from the most obvious reason which is "you don't go trading with your enemy if you don't want to be killed".
Somehow, in fact it helped to open both markets on each other.
The crusades, in turn, helped to change the economic activity of
Christian Europe. The crusades “enabled Western Europe to monopolize
the whole trade from the Bosphorus and Syria to the Straits of
Gibraltar.” Even if they failed to take the holy place from the
hands of Muslims, they politically weakened the powers of the Islamic
states and Byzantine Empire. The Byzantine Empire’s maritime power was
weakened seriously and their merchants now could not compete with the
Italian rivals, which now controlled the Byzantine Empire’s export and
import trades. The crusades also caused the large influx of Eastern
luxuries into Christian Europe, thus stimulating the interest of
people for the trade with the Islamic world. So, it is no exaggeration
to say that the crusades were crucial factor in the revival of
extensive economic activities of Medieval Christian Europe.
As it's described later, the main European ports that were trading with Islamic World were Genoa and Venice. And even if there were some difficulties, a business is still a business.
The trades with the Islamic world at first time were limited because
of religious reason, and because of technical reasons, but gradually
the Italian merchants began to seek profits and the economic
incentives were large enough to overcome religious obstacles for
greater incomes. As a result, the Italian city-states rose as major
maritime commercial centers from 11th century, and the scope of their
trades even exceeded that of the Muslim ports.
I'll quote only two paragraphs more and I'll leave the rest to you, if you're more interested in the trade with Islamic World in overall, not only from the point of it's connection to religious problematic.
Christians and Muslims have been enemies by principles. Moreover, as
the Middle Age was the time when the religion affected the lives of
Christians most significantly, the Muslims were considered evil by
Christians. This aversion of Christians toward Muslims, however, could
not stop the economic interest of the Christian merchants, and the new
pattern of global trade appeared.
The Muslim world indeed acted as an important trade partner of Europe
in the Late Middle Age. They facilitated the European trade and thus
strengthened its economy. Also, they provided the goods that were not
available in Europe, and this fact made Europe a favorite place for
European merchants. The religious principle could not separate the
two. The trades between Europe and the Muslim World sometimes stopped
because of political situations, and were greatly reduced when the
Turkish soldiers occupied Constantinople and destroyed Byzantine
Empire. However, it is evident that the two had long-time economic
connections, and such connectivity helped the European economy a lot.