There are a number of connections that can be drawn here. In some ways, the Progressive Era was a reaction to the needs of immigrants and in some ways it was a reaction against immigrants and their ways.
The immigrants typically experienced very poor conditions. They had to work in hard and dangerous jobs for low wages. They lived in crowded and unsanitary conditions. Part of the politics of the Progressive Era revolved around regulating big business to reduce these problems.
The immigrants also brought their cultures with them and, in addition, formed the basis for urban political machines. The politics of the Progressive Era also involved fighting these things. Many reforms were aimed at breaking the corrupt machines. Prohibition was the main reform aimed at immigrant culture.
In these ways, Progressive politics included tendencies to help and to fight the new immigrants.