Answer:
Hobson's Choice originated at Cambridge University referring to a stable owner named Thomas Hobson who, in an effort to rotate the use of his horses, would offer only one horse to prospective riders. So, it means, "Take it or leave it, that is your choice, this one or nothing." But I assume you know that.
Since suffragettes were women seeking the right to vote; one might link the two by pointing out that women were trying to remove their lack of choice.