Almost certainly, if current trends continue. Matching, of course, an Islamic Europe, and not least an Islamic Britain.
Immigration, which capitalism of course requires be unrestricted, is a factor here. But it is less and less so. The spread of Islam among blacks (with their massively influential popular culture) and Hispanics in the US matches its spread among British youths of Afro-Caribbean extraction, and also among white, middle-class, often female seekers after something more than our decayed, violent hedonism. There are already well over sixty thousand Muslims in the White British ethnic group. Just project that figure over the next hundred, or even only fifty, years. And that's only the White British ethnic group.
We need to re-learn the value of structured daily prayer, of setting aside one day in seven, of fasting, of almsgiving, of pilgrimage, of the global community of faith as the primary focus of personal allegiance and locus of personal identity, of the lesser outward and greater inward struggle, of the need for a comprehensive and coherent critique both of capitalism and of Marxism, of the coherence between faith and reason, and of a consequent integrated view of art and science.
The answer to the challenge of the Sunna is Sacred Tradition. The answer to the challenge of the Imamate is the Petrine Office. And the answer to the challenge of Sufism is our own tradition of mysticism and monasticism.
Liberal Catholics will be the last to see the point.