There appears to be a misimpression among many that a product that features a gluten-free status can be understood to mean that the product is also chametz-free. This is an error. There are a number of examples in which a product can be gluten free and nevertheless chametz.
Products that contains oats, or oat fiber, can be declared to be gluten free and nevertheless be chametz.
Ethanol can be from wheat and is chametz, yet gluten-free.
Vinegar can be made from wheat and be chametz, yet gluten-free.
A biochemical process called fermentation can yield products that are gluten-free but nevertheless are chametz. Thickeners, acidifiers, flavors, and other specialty ingredients can benefit from this process. It is impossible to look at an ingredients label to determine whether any of the ingredients are the result of fermentation.
Soy milk can be produced on equipment that produced oat-milk.
There are plenty of other examples.
To recap: gluten-free does not equal chametz-free.