>How do we make sense of a party that simultaneously proclaims itself pro-life, yet wants to remove roadblocks to capital punishment

Because "pro-life" is a slogan, a sales pitch, a political statement that only tangentially involves the concept of life at all. It's MARKETTING the same way that socialism was selling point of a certain German national socialist political party. (And they did raise wages and rights of workers early on.) Or the "Democratic" part of the Democratic Republic of Congo.

If you even glance at the history, they have their roots in religious ideology which is a-okay with capital punishment (and also against it, depending how you want to pick those cherries).

It's just something they say to get the religious nutters to vote for them. Is a scam artist being irrational when he lies to a mark? Then along came a nuttier nut who actually delivered on that promise and boom, they're all losing elections.