I have a hard time equating the word "conservative" with the word "careful"... It's a synonym, but philosophically speaking (which is what we're doing) conservatives are strong rather than careful. We prefer positions of strength when it comes to defense, foreign relations, etc.
Strictly speaking, conservative as a political description means "disposed to preserving existing institutions and conditions". We are that, too.
You could also include "intellectual conservatism" as the third movement. An intellectual conservative is someone who uses facts, rather than emotion, as intellectual currency in a debate. Opinions, philosophy, political and social ideals... all follow factual evidence. As most of us at FR uphold reason over emotion, I suppose we're all intellectual conservatives of one stripe or another.
I would argue that this is just being "careful". As in 'Better safe than sorry'.
Strictly speaking, conservative as a political description means "disposed to preserving existing institutions and conditions". We are that, too.
That's the traditional def of 'social' conservatism, I think.
And personally, I've seen both Ls and Cs revert to 'emotional' arguments on far too many occasions. I am afraid that is more a matter of personality than anything else.