Varieties of criticism
Conservative criticism has nothing much to do with "left-wing" or "right-wing", because left-wing people are often very conservative, in the defined sense, while right-wing people can also be very radical, in the defined sense. The difference between "radical" and "conservative" has more to do with the belief in whether "a change to something genuinely new" is really possible and necessary. Radicals typically believe strongly that such change is highly desirable and necessary, and that it can be achieved. Their criticism is that there is "not enough" change. Conservative critics, by contrast, are very skeptical about any such change, because they feel the change is really "just another form" of something that already exists.
LGBT rights in Canada
In the House of Commons, four parties support LGBT rights with varying degrees. The New Democratic Party, Green Party, Bloc Québécois, and Liberal Party of Canada are the most vocal supporters of these rights. At its founding, the Conservative Party of Canada was largely opposed to LGBT rights, although some members, typically former members of the Progressive Conservative Party, have supported LGBT rights, including same-sex marriage. Former members of the Canadian Alliance have generally opposed expanded LGBT rights, and a former CA MP was rebuked for calls to re-criminalize homosexuality. Since 2006, the Conservative Party has become a stronger advocate for LGBT rights in Canada and abroad. In May 2016, Conservative Party delegates voted in favour of removing the definition of marriage as a union between one man and one woman from the party's official policy document, effectively changing the party's official position on same-sex marriage from opposed to neutral.