Eh, I don’t think not wanting gambling and amoral behavior to consume society makes me a conservative in any real sense of the word. More just common sense pragmatism, is how I’d put it.
It’s perfectly fine to be for progressive social changes, as long as those criteria are met.
I’d call that a pragmatic approach, not a conservative one.
The other meaning of "conservative", the one that's opposite "reckless".
It should in theory be possible to take a conservative approach to being progressive.
That's likely how most of the middle see themselves (if not in those words) - open to new changes but only if they're fully understood and not drastic.
Conservatives think societies are hard to understand, which makes them hard to engineer, and replacing institutions that work with new inventions needs to be done carefully and slowly.