On the LSAT, yes, this sort of thing is a possibility; on the GMAT, less so.

The above example is meant to show you how common sense can sometimes be misleading when it comes to formal logical statements. But the GMAT will almost always use sentences that make a little bit of sense even outside of formal logic. One reason the statement "Every Republican is not a conservative" is that we know, in reality, it's false; some Republicans, in fact many of them, ARE, in the real world. Now, of course you shouldn't bring real-world knowledge to bear on GMAT questions, at the same time, they don't tend to "trick" you by directly opposing reality like this.

Take the following sentence: "Every stone is not alive."

Clearly, this means that no stones are alive. It's clear because it's true -- it means what you expect it to mean. On the GMAT, you should anticipate that the logic, while it may be weird, won't contradict obvious reality, because GMAT questions tend to be grounded in realistic situations.

However, the book is correct: "Every" means "All." So, "Every Republican is not a conservative" means "All Republicans are not conservatives," and thus, "No Republican is a conservative."

Every = All
Some = 1 or more
Most = more than half