Research over the past decade seems to show that dietary cholesterol doesn't appear to raise LDL levels. Carnists (and in particular self-identifying "antivegans") overextend this research and make a variety of claims regarding cholesterol, including:
I'm not sure how to attack a claim that "cholesterol is a valuable micronutrient that vegans lack". When looking around at scientific papers I can't really seem to find any that substantiates that claim. All I can say is that your body already makes cholesterol in sufficient quantities so it's, on the face, not particularly reasonable, and this claim can't be taken seriously as a reason to abuse animals given the lack of presented evidence.
The AHA (the multi-billion-dollar medical research organization charged with the CPR certification of essentially every healthcare worker in America) puts it in no uncertain terms on their site that cholesterol, in particular LDL, causes heart disease.
The main source of this set of scientific denialism is some version of the "antivegan copypasta" which has serious problems in the papers it cites on the topic.
Regardless, The aforementioned AHA's recommendations for physicians in a recent, comprehensive, and well-cited meta-analysis are as follows: "Dietary guidance should focus on healthy dietary patterns (e.g., Mediterranean-style and DASH [Dietary Approaches to Stop Hypertension]–style diets) that are inherently relatively low in cholesterol with typical levels similar to the current US intake. These patterns emphasize fruits, vegetables, whole grains, low-fat or fat-free dairy products, lean protein sources, nuts, seeds, and liquid vegetable oils." The full paper has some more specific recommendations that include limits on egg and meat consumption. This idea that red meat and eggs lower heart disease is just not substantiated.