This is an interesting what if. Cell arc barely changes at all. Future Trunks explains to the group about the threat of the androids, without killing Freeza. Cell's looks noticeably different.
I say Freeza would still train considering he got his ass handed to him by
and was too afraid to go fight him in this scenario. The emergence of the Super Saiyan proves to Freeza that it is possible for a fighter to appear stronger than his full power. Golden "Mecha" Freeza rules the empire until the healing pods improves to the point where he can regenerate his full body back, in this long time period he also notices the flaw of the Golden form and masters it. Boo arc is identical to it's canonical self. Beerus arc is completely identical, save some dialogue differences between Whis and Beerus at the start. Universe 6 is identical too.
The differences actually start to happen when the Future Trunks arc happens. I'm going with manga Super though. Goku Black goes to Freeza as he's the strongest in U7, (expect for
of course) Freeza recognises him as Goku, Freeza promptly beats the shit out of Goku Black. Future Zamasu manages to heal Goku Black, and he can now use Super Saiyan. At first Goku Black has the advantage over Freeza, but then Freeza transforms into his Golden form. Zamasu teleports him and Black outta there. However, Freeza is aware that Goku comes from Earth, and heads there.
Goku Black is already pretty strong when he arrives on Earth. This is at first similar to Future Trunks arc where the humans are getting killed off by Goku Black, but Freeza quickly arrives. Goku Black initially tries to fight Golden Freeza but gets beaten to a pulp again, Zamasu manages to heal him and Goku Black can now go Super Saiyan Rose. However, this barely makes any difference, and Golden Freeza still annihilates him. Goku Black and Zamasu are forced again to escape Earth. Which leaves Future Trunks and Freeza. Bulma doesn't die, there was too little time for Goku Black and Zamasu to find her, and she manages to create the fuel for the time machine.