Social conservatives appeal to an authoritative government. Are social conservatives not real conservatives?
That's actually incorrect.
SOME social conservatives appeal to an authoritative government.
The issue is people wrongfully attempt to take an ideology that has
multiple segments and suggest that a singular segment is the true one.
You have Social Conservatism, focusing on traditions, morals, and societal lifestyle.
You have Governmental Conservatism, focusing on size and scope of government and the amount of intrusion and power it should have on peoples lives.
You have Fiscal Conservatism, focusing on the costs of operating government and the amount government involves itself in your own finances.
You have Militaristic Conservatism, focusing on the size/scope/strength of our military, our intelligence capabilities, our status and regard within the world, etc.
Those are in my mind your four largest branches from the baseline of "conservatism". Someone who is extremely socially conservative but who is rather weak regarding Governmental conservatism is likely to trend more authoritarian, as they do not have the conservative aversion to government intervention so intead us the government to enforce those traditions, morals, lifestyle choices, etc.
On the flip side, one could be a social and governmental conservative, and feel that those traditions or morals should be instilled by preventing the use of government to enforce things onto people that are contrary to those traditions or morals, or that they should be instilled from a more personal level with the government staying hands off save for in places its absolutely necessary.
Depending on how strong or weak they are in any particular portion of conservatism can tip the scale as to what's acceptable and what's not.
Its possible to be socially conservative and not be authoratarian. Its even possible to be socially conservative and libertarian. The "authoritarian/libertarian" deliniation comes much more out of their place on the governmental scale rather than social.
There's not only one type of social conservative, and attempting to lump all conservatives as those who feel the government should forcefully involve itself into how people live their lives is a grossly innacurate and ignorant of reality statement.