I have mixed feelings on this. In part because I want to be pedantic but also because I think there's multiple levels here. To be succinct, because that first sentence was wishy-washy, I don't think it's wrong to identify Islamic terrorism as being associated with Islam. THAT BEING SAID, it's not productive to have a public discourse from this perspective in my opinion because the general public is emotional and whimsical and so giving them a complicated debate only invites the opportunity for miscommunication and the development of hate in my opinion.
The reason I think it's important to identify terrorism committed in the name of Islam, Nazism, Christianity, etc. with their respective belief systems is because it empowers us to ask 'why'. Why are so many terrorist organizations affiliated with Islam, RECENTLY SPEAKING? Why has white supremacy become more visible in the American social space including the pre-charlottesville social space? I don't have the end all be all answer. But I think asking the question is important because whatever the true answer is, I think it's fair to say that it's probably regionally rooted, potentially linked to the economics of certain groups rooted in those regions, and because of the regional nature of many Islamic terrorist groups and white nationalist groups, I think it's fair to say that there is a cultural BUT NOT UNIVERSALLY CULTURAL element to it. I would make a similar assessment of the IRA in Ireland, Christian terrorists in Africa, and by now you can probably see where I'm going with this. Acknowledging the affiliations of these organizations and their beliefs is important because it explains THEM. It doesn't inform us about their beliefs, but it allows us to analyze why they have chosen to affiliate with those beliefs in a hopefully honest fashion.
None of that is meant to imply that Nazism should be viewed as American, or that Islamic Terrorism should be viewed as a sub-element of Islam, but acknowledging that these contexts exist with regard to SPECIFIC ORGANIZATIONS is important in my opinion because the root of these issues is often multifaceted and can only be combated, in my opinion, with a comprehensive understanding of these groups and their spiritual as well as political influences.
Edit: I will acknowledge when I edit an argument in the face of something that someone has pointed out. This post has already been heavily edited for my own satisfaction however because while modern examples of significant terrorism are obviously not evenly distributed across cultures, that does not mean that one culture is implicitly prone to terrorism and I'm trying very hard to keep my grammar and framing of arguments as neutral in that respect as possible while acknowledging the current configuration of terrorism, hate, and extremism across the globe.