It's not that they are second class citizens. It's just that people with dual-citizenship can't hold some government positions. Lots of countries have similar laws.
...which, in my view, makes them second-class citizens, in that they do not have the same privileges as other citizens.
But then I'll admit my bias, because Canada's Constitution explicitly protects various rights regardless of citizenships held:
Charter, s. 3:
Every citizen of Canada has the right to vote in an election of members of the House of Commons or of a legislative assembly and to be qualified for membership therein.
Note: nothing about not holding other citizenships.
Charter, s. 6(1):
Every citizen of Canada has the right to enter, remain in and leave Canada.
Nothing about not holding other citizenships.
Charter, s. 15(1):
Every individual is equal before and under the law and has the right to the equal protection and equal benefit of the law without discrimination and, in particular, without discrimination based on race, national or ethnic origin, colour, religion, sex, age or mental or physical disability.
National origin (which often implies multiple citizenships) is explicitly protected.
For that matter, two of our last three Governors General (Adrienne Clarkson and Michaëlle Jean) were foreign-born, in Hong Kong (under British rule) and Haiti, respectively.
So that's why I say that Australia has second-class citizens (if you hold another citizenship, you can't serve in Parliament). It's why I say that the US has second-class citizens (if you're not natural-born, you can't be President or Vice President).
And, for that matter, the Conservatives tried to create second-class citizens, by passing a law that allowed the government to strip Canadian citizenship from people holding multiple citizenships who were convicted of certain terrorism-related offences, but the Liberals have put a moratorium on doing so (it's at ministerial discretion, not automatic), the only person stripped of his citizenship in this way has had it restored by the courts (I believe, or it's in the process of going through the system), and at this point it's almost certain that either it'll be repealed legislatively or declared unconstitutional by the Supreme Court.
So I find the notion that not all citizens are equal in their citizenship repugnant.