There are a fair few tory members (not just backbenchers) who are against May's fetish for ripping up human rights bills and installing a camera in every bathroom.
DUP are fundamentalist christian hard-right tories, but on the other hand they're in Ireland and know a lot about the bad side of state power (despite nominally being on the side of the British government)
Indeed, and this is likely to be a major sticking point with May. You can't really tell any kind of anti-immigrant story with a fully open border, but a fully open border is what peace in Ireland needs, and the DUP fully recognize that.
It's important to understand that support for moderate parties in Northern Ireland has only collapsed because both Sinn Fein and the DUP are seen as being fully committed to the peace.
DUP are fundamentalist christian hard-right tories, but on the other hand they're in Ireland and know a lot about the bad side of state power (despite nominally being on the side of the British government)