"sensible conservative groups"
con·tra·dic·tion
/ˌkäntrəˈdikSH(ə)n/
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noun
a combination of statements, ideas, or features of a situation that are opposed to one another.
"the proposed new system suffers from a set of internal contradictions"
a person, thing, or situation in which inconsistent elements are present.
"the paradox of using force to overcome force is a real contradiction"
the statement of a position opposite to one already made.
"the second sentence appears to be in flat contradiction of the first"