Incompatible progressive beliefs

JobCentre

Walking home this evening the incompatibility of two commonly held progressive views dawned on me. The first is that immigrants often do the jobs that Brits won’t. The second is that only a small number of welfare claimants are spongers. The majority genuinely can’t find work because the government isn’t doing enough to create jobs.

If the first view is correct then there must be a lot of British people who could work but choose not to. And if the second view is correct then the number of immigrants doing jobs that Brits won’t do is very small. So why is it so often mentioned?