I thought it was that composer Beethoven wasn't related to the modern Beethoven's who were related to the originator of the name.

So composer Beethoven's branch is the "bastard" branch for lack of a more apt term.

In terms of culture and religion it was pretty much the same. There may have been different names for particular gods and different modes of worship but overall it was the Etruscan pantheon that was venerated.

There were language differences, most of the rebellious Italians spoke one or another sabellian language and the Etruscans (who did not rebel) spoke Etruscan. Most everyone probably spoke Latin or enough of it to get by. The elites were certainly fluent in it as well as Greek.

There was significant intermarriage among the elites of all the various tribes and romans. Culturally if a samnite married a Roman, etruscan, lucanian, bruttian they probably would not have any more surprised by anything they did than a Californian marrying a New Yorker.

The main problem was that romans had started getting particular about who they were letting become citizens. A hundred or so years before and non romans absorbed into the Roman state would have gotten citizenship with relative easy (look at the families of Marius, Pompey and Cicero) but by the social war it was a very guarded. The Italians felt, quite rightly, that they were being taxed equally to romans, served in the army equally to romans and suffered equally to romans (look at Jugurtha and Mithridates massacres of Italians) they should get equality under the law.

Some Romans agreed with this, there was ongoing debate in the senate but Optimate VS Populares partisanship bogged everything down to the point where the Italians felt they had no other options.

In the war itself Rome's greatest weapon was citizenship, its how they prevented certain tribes from joining the Italians and how they brought rebellious allies back in the fold. The Italians just wanted the full benefit of the empire they helped conquer.

Would they have gone full independent? If the romans had been unwilling to compromise quite probably. But It would have been an Italic state or a Roman one, Italy wasn't big enough for two states by that point. If the Italians had won they quite probably would have absorbed the empire as it was and used the same system of governance, just swapping out the romans at the top with Italians and the provinces probably wouldn't have noticed a difference. If the province's rebelled the Italians would have acted just like the romans would have, they would have considered that territory just as much theirs as the Roman Republic did.

Edit for typos