I agree with you, Jess. There's even muddled thinking about migrant workers. Some of them come to work in the NHS, schools, IT, engineering etc and, thank goodness they do, because we have chronic skills shortages. Generally, it seems that skilled workers don't suffer that much discrimination. They're not 'taking anybody's jobs' and are being paid the going rate in skilled jobs.
However, if you go into parts of Fenland, especially Boston (the highest voting Brexit area in the country), attitudes are different. Workers are often employed by agencies and do drive wages down. The agencies sometimes use a loophole, which allows them to pay 'local' (ie country of origin) rates, which is below the UK minimum wage. Their English is often poor and there's a tribal mentality amongst the immigrants themselves and local people. Waffly liberal talk is going to fall on deaf ears, so Corbyn is right to open the discussion about barriers to integration and do something about it.
Good Morning Wednesday 1st May May Day