Please read this. There’s no social barrier for Buddha to declare rebirth, kamma as false should he personally realize it is false. But he declared them to be true.
The Buddha would not had taught things which hinders realization.
As wrong views includes actively not believing in rebirth, that is hindrance.
Jīva if seen as soul is deemed as not existing, so there is no meaning to the question of soul same as body or not. The usage here is not citta.
The 5 aggregates model can clearly been seen that mind and body can be grouped separately. Dependent origination maps how they interact with each other. Formless realms indicated that it’s possible for mind to exist without body. It’s still not considered soul because mind is impermanent.
It’s good to reflect how much the ideology of scientism/materialism/physicalism is behind all your disbelief in rebirth. See the feelings accompanying the views. That’s the source of attachments to wrong view.
You see Buddhists like us can still can strive for enlightenment having faith in rebirth. You see enlightened ones like Buddha acknowledging rebirth exist for unenlightened beings.
Let me speculate a bit.
The fear of acknowledging rebirth as true pushes a bit more towards eternalism view a bit, but it’s ok, gradually, one comes back to the middle path. The fear is being responsible not just for this lifetime. But for all potential future lifetime if one doesn’t attain to liberation in this life or at least stream entry. And then the pressure for attainment is much greater.
Well, apply relaxation techniques. And you can also see that yes, things are way more serious and stakes are so much higher that it’s nothing to become a monastic. Nothing much is sacrificed. It’s worth it.
Not believing in rebirth is like an ostrich putting it’s head under the sand. Not wishing to face empirical facts, reality. When the rebirth evidences in the OP clearly has this phenomena. Independent of Buddhism, objectively verified. Thousands of cases. Many pre internet, so basically no way of the kid or family cheating. Even with internet, it is not easy to cheat. So many cases involve hard to dig out facts, not found online.