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.
Social conservatism
Social conservatism in the United States is a right-wing political ideology that opposes social progressivism. It is centered on the preservation of what adherents often call 'traditional' or 'family values', though the accepted aims of the movement often vary amongst the organisations it comprises, making it hard to generalise about ideological preferences. There are, however, a number of general principles to which at least a majority of social conservatives adhere, such as opposition to abortion and opposition to same-sex marriage.