There is simply no empirical evidence that immigration really has this consequence. The welfare state has been fought for by the working class. The rich, or more precisely the capitalists, will always try to search for a reason to undermine it again. Immigrants are just a useful scapegoat in that regard. With such arguments they can split the workers' movement along ethnic line. We must counter it with solidarity. The working classes in all countries have more in common with each other than with their respective ruling class. An effective struggle for reforms under capitalism (let alone to replace capitalism with socialism) requires unity on the part of the working class.