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.