I think that the engineering mindset (adherence to the scientific method, evidence based decisions, planning for the future etc..) is one that is definitely shared by both groups at least.
But you can absolutely get away with building software without proper engineering standards. It's not so easy to build bridges that way.
I'd wager that it is but the stakes for failure are too high to wing it (hopefully).
Imagine:
We want to build a bridge that spans N meters. We don't know how to do it but we can go look at an existing bridge and copy it. We might not understand metallurgy / physics that well, but we talk to suppliers and ask for "steel of this shape and size". Ditto cables, concrete and everything else.
Probably, provided we're not scaling up or changing the design too much, it would work just fine.
When software goes wrong, the effects are more often than not, intangible. When mechanical engineering or electrical engineering goes wrong, people can die.
Software can obviously kill people too, it just happens less. Then industry practices revert to the mean due to cost cutting.