Perhaps you can explain to me why I would wish to affiliate myself with people who do not agree with my political philosophy. That one just goes right by me.
Because we live in a 2 party system with no opportunity for coalition government. You CAN join any number of right of center party's anytime you'd like, but they won't actually win elections. But that's your choice. If you most value political purity over ever having a chance to govern, then sure, join a 3rd party.
In our 2 party system the political party's are very big tents - filled with all sorts of competing interests. The candidate that makes it through the primary process has to appeal to a plurality/majority of a wide range of views.
Politics is as much about defeating the opposition as it is about advancing your own particular set of issues. Sometimes just stopping the left is victory enough. 3rd party's can't do that - in fact they act as a spoiler and often help ones political enemy.