Acting in a way (by a minority, some of which are in power) that is clearly against the teachings of the religion doesn't mean it's false. It's the other way around: it makes their actions a sin. If you take a wider look you'll see that the majority are trying to adhere to the true teachings, which when implemented on a large scale you get what is known as the Golden age of Islam: a period of over 1000 years of prosperity, compassion, and advances in almost every aspect of life, some of which is still benefiting all humanity until today.