I'm not convinced that the labor movement would agree with that statement.
I would agree that the Democrats and Republicans have not completely switched positions in the past century. For example, the late 19th and early 20th century Republicans were imperialists, while Grover Cleveland refused to annex Hawaii. Thus, with respect to dovishness/ hawkishness, the parties seem largely the same. On the other hand, however, the parties have indeed experienced tremendous change, especially on social issues.
that's actually because the ideological position on this issue switched. Back then, conservatives took an isolationist view, while liberals were interventionist. It's not the only issue that has switched ideologically. In the 19th century, liberals were calling for prohibition or greater restriction on alcohol, conservatives were strongly opposed.