this is a very pessimistic view and not really supported by reality. if islam has won, you'd be under sharia law by now.
islam is currently being rejected and overthrown in Iran. its being actively resisted in most western nations, and the usual epithets from islam's usrful idiots, aka progressives, are laughed off now. being called racist, nazi, fascist, etc carries no weight. indeed some almost view it as a badge of honor, which can kead to its own issues.
what is true is that islam has declared war on the west and invaded in great numbers., whilst our politicians were asleep at the wheel. others actively encouraged it thinking they would be gaining perpetual votes (see Minnesota for details).
there are 2 main reasons why we have this problem.
1. the west has eradicated faith from all areas of life and replaced it with nothingness. unfortunately humans don't exist without some kind of faith and so something will fill that void. islam has done that to some degree and many have welcomed it, happy to see Christianity fall away. but be careful what you wish for, which leads to the 2nd reason;
2. westerners don't understand islam. it is not a religion, it is a death cult. they openly worship, glorify, and seek death. they have a doctrine of taqqya which says its good to lie if it will advance their cause. and their cause is not to coexist with other cultures or beliefs, their cause is to eradicate all other beliefs.
but this has happened before. it just took 400 years and a lot of bloodshed to free the Iberian peninsula last time, lets hope peoole wake up before we have to repeat that.
the Crusades were about freeing Eurooe from islam and driving it back to where it came from. tolerance is the problem, not the solution. we don't allow nazi shrines, we must similarly ban mosques.