The problem is that Alexa isn’t actually parsing the meaning of the total phrase, she’s taking each individual word as it comes. With that context, she would just as easily interpret your phrasing as “thing with thing on the side”. You’d still get chive crackers, honey crackers, peanut butter, and cream cheese.
Edit: I thought about this a bit more, and it seems to me the only way Alexa could actually understand what you wanted is if you said “chive cream cheese crackers” or “peanut butter honey crackers”. You have to implicitly make it one item and not a potential combination of multiple items.