>>63948168
I don't know about elsewhere, but at least regarding English, it seems the church didn't really attempt to suppress them and actually used them too (two notable surviving examples being the most decisively Christian inscriptions on Saint Cuthbert's coffin and the Franks Casket); to my understanding they just got organically phased out over time, not just because of religious reasons but also because it's what everyone on the continent was using.
There was actually a transitional period of several centuries where English texts used a hybrid system, retaining thorn/ᚦ (th) and wynn/ᚹ (w). Examples also exist of runes being used in latin texts as ideographs for whatever their name was, such as writing mann/ᛗ (m) as shorthand for "mann" rather than writing the whole word out.

On a tangent, I'm 100% convinced that written English would greatly benefit from reintroducing thorn/ᚦ and ing/ᛝ, because their respective sounds (both very commonly used) take multiple letters to represent in the latin alphabet, making it less efficient with time, effort, and space.
An extreme example of what I mean is the title of John Carpenter's 1982 film "The Thing", which could be condensed into just "ᚦe ᚦᛝ".