"I think it is easy to support the general EU objectives of free movement of goods, services and people."
Really? That is most of the problem. When the border with Poland opened 2 million Poles crossed going outwards. The number that crossed inwards looking for work? - could probably count on your fingers.
So sure Poles will support those objectives but the people in the countries they went to not so much because at least some of what the Poles gained was their loss.
Free movement forces an equalisation of living standards and that hurts people in the wealthier members and very unfairly. The rich get cheap servants and labour for their businesses the skilled workers get their wages depressed and the unskilled end up on the dole.