Much of the popular usage of "religion" in the negative isn't relegated to any particular denomination of evangelical Protestants, and if you consult theologians in that denomination they wouldn't use it in the negative. Usually, simply quoting James 1:27 gets them saying, "Oh, well not religion like THAT."
When used in the negative, they tend to mean something like, "A system for becoming right with God by your deeds," or "A church or group of Christians preoccupied with rituals, traditions, or doctrinal precision to the expense of a personal relationship with Jesus and loving others."
Evangelicalism is broad. In fact, that is what makes it evangelicalism, as opposed to evangelical Methodism, evangelical Baptist, etc. Evangelicalism is a kind of umbrella category to describe a diverse set of Christians who share a few core features in common concerning Jesus, scripture, and salvation.
Using "religion" in the negative is more of a popular level opinion than a technical term. A common refrain is, "Christianity is not a religion, it is a relationship." I, as an evangelical, disagree with the statement but I get the sentiment.
It's often a loosely used term, much like when a Christian says, "God told me X." If you asked them, "So, when you say that God spoke to you, do you mean that you were thinking and praying about it and you had a really strong impression that you felt comfortable with?" They respond, "Yes, exactly! God just wouldn't let it get off my mind." Rarely would you be told, "No I mean that I heard an audible voice that told me this." Usually, "God spoke to me" is used loosely, and to people with careful distinctions about divine revelation and providence, this manner of speaking is reckless. Yet, it's still a manner of speaking that occurs on a popular level.
I think the same thing is happening with the religion/relationship dichotomy.