Nah, there's been several studies done showing that conservatives tend towards valuing group loyalty. Group loyalty (aka tribalism) isn't innately a bad thing; it's a necessary component for a working society. However, it can also offshoot into jingoism, xenophobia and other forms of intolerance. On the positive side, group loyalty (and expectations within the group) tend towards stability and predictable results which are things more prized by conservatives than liberals. But it's a cycle as well -- since your group provides stability, anything perceived as threatening your group threatens your stability and you're much more prone to react with hostility towards the "other". Which then leads to people flipping their shit about having to choose between Spanish and English at the ATM and going on about how immigrants are ruining the country.
There's a lot more that goes into our political psyche of course than just group loyalty and a number of casual interpretations of the studies overstate the result ("liberals only care for fairness and lack of harm" as though they don't care about law & order, family groups, tradition, etc) but the fact is that, all other things being equal, if you display a strong sense of tribalism you're more apt to think like a conservative.