I dont really care what Coin base knows I just dont want them sharing the info
They are surely not collecting information for fun, are they?
The fact that they are gathering information about you means that they will share it somewhere once authorities request for it.
Since you are using Coinbase specifically to just buy Bitcoin for now, why not opt for p2p exchanges that do not require KYC like Localcryptos, Bisq, HodlHodl?