At war with an Ideology

I usually try to limit my posts to things about which I have some knowledge or about which I have read substantiated articles. This post, however, is more of a wondering and I have absolutely no idea if this has merit.
I'm wondering if the old way of responding to an international event, attack, whatever, is just that, an antiquated response. Through the years, our enemies have been countries or political entities, distinct bodies we could attack, conquer or subjugate, and cause to back down and behave in ways we deem acceptable as was the case in WW I & WW II, the Korean Conflict, etc. It was even, probably, the case in Vietnam even though "our side" didn't win. We knew who were at war with -- Germany, Italy, Viet Cong. We could shoot them, bomb them, kill them, etc.
Today’s enemy is ideological. They have no geopolitical boundaries, no readily identifiable location, not even a reliable way to isolate them. When we attack them with conventional warfare, the response is not conventional warfare, not even the counterinsurgency we saw in Vietnam. It is what we have come to see as seemingly random terrorist attacks.
It is becoming apparent that what we have been doing with rather conventional warfare in Iraq & Afghanistan cannot stop this new enemy. Taking off our shoes and swabbing our hands at TSA airport checkpoints does not stop this enemy. All our current techniques are no more successful against ideology than it was in preventing Ebola entering the U.S. While the ideology has some connection to a particular religion, banning that religion from our country, or any country, cannot stop it and can inflame it as well as being every bit as dreadful as Japanese internment camps or the Holocaust. And, because it is ideological, but not descriptive of the entire religion or an entire country, we can't blanket bomb the entire Middle East and eliminate the ideology.
So nothing we have done or proposed has been effective. If anything, these ideas have fed the hatred and violence. Now, the hard question. What can we do? If I understand, the ideology at play is similar to the Christian Dominionist ideology that Jesus cannot return until Christians have control of the socio-political systems of the world and return to a literal interpretation of scripture, Allah will not be satisfied until Islam with a literal interpretation of the Quran is the religion and law throughout the world. At this time, the Dominionists are approaching their ideological goal politically. The Islamic fundamentalists are taking a violent approach to conquer. I don't have the answer. I don’t agree with literal interpretation of any scripture. I don’t see violence as an answer any more than I believe we need to conquer. I'm looking for a way to end the situation.