Many rugs are heat treated and will not shrink. However bindings may be of polypropylene (like plastic) and can suffer damage in hot water. It’s wise to avoid using water above 40c. Avoid hot or warm water, as some machines will use a very hot cycle, (some up to 90c+ )- excessive hot water will damage the polypropylene binding, which will melt/change shape, it tends to shrink and cause the binding to bunch up.
Never use a clothes dryer, as the high heat will melt or damage the fabric and polypropylene bindings and straps causing shrinkage and distortion of shape.