I can recommend readsettlers.org for an in-depth view at race-relations over the centuries.
The gist is that race is defined by an ingroup and is pretty flexible depending on who they consider to be part. Irish people weren't in when they were an economic threat to the other laborers. Now they part of the higher laborclass so they are "in". So depending on the relation of the privileged laborclass to a particular nation that nation might be considered white or not. Exceptions and ifs and buts apply liberally ofcourse.
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