The CDU always has contained everything from centre-left to far-right, as long it’s compatible with democracy. Their right wing is about en par with Reagan, their left wing with, dunno, Harris, status quo liberals in general. They’re not about to abolish public healthcare, gutting unemployment benefits OTOH is up their alley. Social conservatism wise they tend to brake a lot, but aren’t prone to be regressive, like wanting to roll back gay rights or something. Or, differently put, they won’t be any more conservative the EKD which is absolutely fine with reverends having gay sex in the vicarage as long as it’s monogamous.