Preheat the oven to 350°F. Lightly grease a 2.5-quart or 9x9-inch baking dish.
In a large bowl, mix together cream cheese, sour cream, and mayonnaise until smooth and well combined.
Stir in garlic, the white parts of the green onions, soy sauce, sriracha, and Worcestershire sauce until evenly mixed.
Gently fold in the crab meat, Monterey Jack cheese, and mozzarella cheese, being careful not to break up the crab too much.
Spread the mixture evenly into the prepared baking dish.
Bake uncovered for 25–30 minutes, or until hot and bubbly around the edges.
Remove from the oven. Scoop and gently spread the red pepper jelly or Thai sweet chili sauce over the top. Garnish with the green parts of the onions, wonton strips, and sesame seeds if desired. Serve warm with wonton chips or pita chips.