Most invaders in history did not violently impose their own philosphies and idealogies on day 1. Generally you let the conquered people keep their philosophy and religions to a big extent until the population has adopted it naturally through softer means, Islam specifically has a few verses around tolerance for "people of the book". Islam for example puts higher taxes on the non-muslims and people will then naturally gravitate towards Islam. Once the population has islamized to a higher percentage the islamic ideology will be implemented more deeply.