Definitely not to the center, they had to call themselves center in the post revolution period in order to survive.
You may be aware that one of his founders Freitas do Amaral, was a vocal opponent of the Iraqui invasion and now is the Foreign Ministry of the Socialist government as an independent. So i guess it's safe to assume they have been drifting to the right.
Anyway, they were the only party with aspirations to power for the disenfranchised fascists.

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.