I find your question a little ambiguous. The definition of 'Islamic world' and 'powerful polytheistic people' can vary.

Anyhow, I will answer this to the best of my ability.

India, particularly North India, was very much under Islamic rule for much of its medieval history. It's fairly obvious that they weren't successful in converting the majority of the local Hindu populace.

Now, if you wish to talk about the current boundaries of the Islamic world, i.e., current Muslim-majority countries, there are quite a few examples.

One example is the Nuristani (literally people of the land of light) people of Afghanistan. Previously, there were known as the Kafiristanis—people of the land of infidels. The Emir of Afghanistan subdued them in the late 19th century and converted them to Islam, after which their name was changed.

A branch of these people still live on and carry on with their faith on the other side of the border—the Kalasha of Chitral, in Khyber Pakhtunkhwa province of Pakistan. Around half of them have converted to Islam, but the other half carry on with their polytheistic faith.

There are Hindu minorities scattered throughout Pakistan, Bangladesh, Malaysia, and Indonesia. The island of Bali, in particular, has an overwhelmingly Hindu-majority population. Western Java too has a large Hindu minority. Borneo has large Buddhist and animist populations.

Even in Muslim-majority islands of Indonesia, animist, Buddhist, and Hindu rituals survive in practicing Muslim populations. These are known as Kejawen. It's not uncommon in rural Java to see people going to the mosque and worship forest spirits later. Suharto himself was a proud follower of Kejawen, I believe.

While they don't really fit into the Pagan/Polytheist category from the Islamic point of view (pragmatic as it tends to be), I'd point to the Zoroastrian nobility of northern and northeastern Iran (Tabarestan and Khorasan), the Karen and Bavand dynasties, who were instrumental in their support of the 'Abbasid revolution and held out until the mid-9th century. I have a brief-ish writeup on them here with links to further sources, as they're not super-well attested. The Sasanian royal family also escaped to China, were granted an army by the emperor, and re-conquered some territory in Central Asia, ruling until the early-mid 8th century.