Years ago my IFB church removed "Fundamental" from the church marquee. The reason? The board did not want to become associated with Middle Eastern fundamentalism. And though it best to identify the Church as First Baptist only. Was this sound judgement?
If so, what other appearances of evil should we disassociate ourselves from. Politicians? Service Clubs? Masons? Etc., etc?
They might not allow officially documented membership since they are eternally secure Arminian Dispensationalists. But they do not practice closed communion. And the general tone of preaching is not doctrinal and bent more towards abstinence and separation.
Two serious misunderstanding are apparent in the OP.
#1. "Avoid the appearance of evil" does not mean to avoid anything that might appear to be evil even though it is not. It means "every time evil appears, avoid it!"
#2. Christian Fundamentalism is not about Islam, and only an idiot would think it was. Christian Fundamentalism is about the fundamentals of the faith once delivered to the saints.
1. The Deity of Christ.
2. The Virgin Birth.
3. The Blood Atonement.
4. The Bodily Resurrection.
5. The inerrancy of scripture.
Fundamentalism is not always about the fundamentals of the faith, at least not in practice. I will not lump all fundamentalist churches together but the ones I was exposed to in the North East held to similar beliefs that separated them from their mainline Baptist brethren. KJVO, card-playing is of the devil, no dancing, ultra-conservative female wardrobe, Tim LaHaye brand of Dispensationalism et al. The Bible college I attended was joined at the hip to these type of churches. As part of our church ministry outreach program, I visited many of these churches. Now, perhaps that was just one face of what is termed "Fundamentalism". In your part of the country, it may be different. What I do know is the type of Fundamentalism I encountered does a very good job of turning people into either a) Legalists or b) atheists.
They believe the "fundamentals" as always. But people view fundamentalism differently today. Because of the evil associated with the term. Linked to Middle Eastern fanaticism or "Fundamentalists" extremism.
I can see it both ways. But these are as abiding in the "fundamentals" as any I've been exposed to.