Much more to the right and less to the center. Their populism tends to hide the ultra-fascist ideology of some of their members.
Paulo Portas is a neocon with very shady ties with the current US administration and some of the ultra-conservative lobbies and think-tanks in Washington.
Others, are just plain Taliban-Christians.
Another wing is strongly "nationalist" yearning for the days of Salazar and Colonialism.
What is left are some neo-liberals (like Bagão Félix for ex.) who you might put to the center-right but not representative of the true center.
Their populist wing borders fascism, true, but you may be aware that the figurehead that made them turn even further right, Manuel Monteiro, left in order to make his own party, so far with little relevance.
What you call taliban christians has to be put into context. Yes there are some members of, say, Opus Dei, but you can find them also in PSD or even PS. Although they are very vocal on "pro-life" issues, and also about the "institutional role of the curch" in portuguese society, i still belive they mostly adhere to democratic principles. Especially under the current leadership, considered weak by the "neo-con" faction.
There was a split?
How much did the Monteiro formation receive in the last elections - or was the split after the 2005 elections? *Lunatic*, n. One whose delusions are out of fashion.
Now that you clarified a few things our opinions are much closer than I thought. I know how hard it is to express all your ideas in a few paragraphs.