I don't think I can put it any better than this:
"Various objections are levied against the oath of allegiance: objections to the religious loyalties still implicit in the oath; republican objections to the requirement to pledge allegiance to the Crown; objections that the oath contains no pledge of duty towards the people, or towards democracy. There are also objections to Members of Parliament having to take an oath at all."
The Parliamentary Oath RESEARCH PAPER 00/17 14 FEBRUARY 2000, House of Commons Library
http://www.parliament.uk/commons/lib/research/rp2000/rp00-017.pdf