Any ideas why mayonnaise makes me want to puke even if I'm not allergic or intolerant?

Adverse reaction. Mayonnaise is made from egg, mustard, lemon juice, oil, vinegar, etc... It might not be the typical allergic reaction but there is obviously something to which your body reacts adversely. You could try to pinpoint which exact item or you could try separate brands. You might want to even find your own recipe and keep it as simple as possible. That might be an alternative.