Coconut oil is only about 92% saturated, and is often still hydrogenated. One particular extraction process, RBD ("refined, bleached, and deodorized"), gets nearly all the oil, but requires further processing.
The dangerous types of trans fats (yep! they too come in different kinds) are a side effect of partial hydrogenation, and appear to be trouble even in very small amounts. This "trouble", from a cholesterol perspective, is an decrease in HDL and an increase in the small, dense LDL particles that contribute to heart disease. (While saturated fats raise LDL levels, the increase is mostly in larger, "fluffier" LDL particles.)
So, Sarah's concern is valid. I'm also not at all surprised at the 3-month change; swapping out grains (a whole different topic!) and unhealthy fats can cause significant blood lipid changes in only a few weeks. The problem for most people is identifying which ones count as "unhealthy", particularly as oversimplifying issues (e.g. cholesterol=bad, LDL=bad) can often lead to incorrect ideas taking root.