It's unclear how much influence Old Italic alphabets had on the various Runics though it's generally thought that Etruscan was a shared ancestor. There's some theories that some of the similarities are the result of co-evolution or repurposing of found letter a la Tsalagi.

For example, Danish Futhark uses the character for 'm' that's used as 'ph' in Etruscan (later to become greek 'phi'), obviously not a morphological change but a repurposing.

Another example, Etruscan 'sh' seems to have disappeared due to confusion with a simplified 'M', which is similar to 'e' in Elder Futhark and 'i' in Gothenburg Runes.

These may have simply been "loan" glyphs, adopted to fill some phonological need, in the way that English doesn't have letters for 'sh', 'ch' or 'zh'.

Most of the morphology seems wholly unique in early Runic scripts, hinting at their uniqueness. But again, as Sequoyah demonstrated, loan characters often are used in more "obvious" ways like as a syllabary.

There's later forms of Runes that borrow more heavily from Latin scripts, and these also seem to be more regularized and simplified over the less standard earlier scripts.