How could buffalo chicken dip be stabilized?
I would suggest making this on the stove top, or in the microwave, instead of in the oven. What is happening is that the oil from the cheese separates from the rest of the dish.

If you are using bottled salad dressing and cream cheese, there is already many thickeners/stabilizers in those. (Xanthan Gum, Guar Gum, Carob/Locust Bean gum)

I suggest that you slowly melt the cheese, along with the cream cheese &amp; salad dressing on low heat. An immersion blender would help to make sure the lumps are gone, after adding the hot sauce, but before you add the chicken (as long as you want to have the chicken texture).

From my experience, the oily separation with the cheese is caused by it over cooking. If you aren't a cheese snob (I am), you could substitute Velveta cheese for the cheddar/jack cheese. Do you remember their commercials with the oily gooey messes with cheddar vs Velveta? It is the same principle at work here.