In California we went to the "top two" primary; that means the top two vote getters in a primary go on to the general election, not the top one of each party. Now I don't particularly like this - it's not good for third parties, and in counties which are largely one party or the other, you can end up with two people of the same party going to the general election.
This happened in my county - 2 dems, 2 repubs, 1 independent ran in the last primary for state representative. The two repubs were the top two vote getters; one of them was heavily Tea Party, the other was just conservative.
So in this case - the TP'ers didn't have their way. The TP candidate won the primary -but in the general election, enough of us held our noses and voted for the non-TP guy (since we didn't have a candidate in the race) that the TP candidate lost.
So I agree in most cases the evangelical minority or the TP minority can use the primary to make a candidate bow to them - in some cases, it doesn't work.