Is this the main evidence?
Not really, no. In an interview in the FFX Ultimania Omega from 2002, Yoshinori Kitase and Kazushige Nojima had mentioned that a concept connecting X and VII would be developed over time. It isn't something that just remained in interviews, though.
In X-2, we got Shinra and his idea to siphon energy from within the planet. Then we got the interview from the X-2 Ultimania where Nojima explained that Shinra worked with Rin to try developing the concept, but that his descendants would be the ones to successfully implement it, many generations later on VII's world.
In X-2: International+Last Mission (which came out after the X-2 Ultimania), it's mentioned that Rin and Shinra had been working together on something (clearly a reference to what Nojima was talking about).
Then in Dirge we have the Shera's interior, which is strikingly similar to those of the Al Bhed airships from X and X-2. In addition, an engineer says the ship is an ancient relic.
It's clearly not something the Cetra would have had. If they didn't even chop down trees to make houses, they wouldn't be building airships. The ship is a blatant element of the connection between X and VII.
Novus said:
Do you mean just the Shinra family (or crew) or the entire human population of Gaia descend from the Shinras/ random members of Spira.
The Spirans likely bred with the Cetra who decided to stop being Cetra. Remember that when Sephiroth talks about the Cetra in Nibelheim, he mentions that some gave up being Cetra to be regular humans and live easier lives.
Those Cetra who became normal humans probably did so after the Spirans' migration introduced things like leisure and technology to them.
Novus said:
Why would they be living in such a tip? Only just discovering electric power a thousand years after, it would have to be for no one to remember that their descendants traveled through space lol.
Not hard to picture since people don't even bother with remembering things that happened in their own lifetimes or that of the previous generation. The names of the towns that became Midgar are no longer common knowledge, and Midgar itself hasn't even been around for forty years. There doesn't seem to have been much record keeping done of the world's history until very recent times.
The more advanced technology the Spirans brought with them was probably lost a thousand years earlier when Jenova attacked and sent people running for the hills.
