Parliament can do anything, if it has the will and the fortitude.  One small example:  the Harper Government attempted to amend the Supreme Court Act retroactively with respect to Justice Nadon.  The SCC did not say that a retroactive amendment was not permitted - it said that an amendment to the Supreme Court Act is tantamount to a Constitutional amendment and therefore required the consent of Parliament and the Provinces.  Amending the Citizenship Act is not a Constitutional amendment.

I don't say it would have been easy, not at all.  I do say, however, that it could have been done if Trudeau stood on reasonable principles.