I'm curious if privacy can be done in a way such that it protects the identities of the transactions (both in terms of btc address and personal identity) while still preserving the open-ness and transparency of the current system?
This depends on your definition.
There are privacy-enhancing technologies available such as CoinJoin and Reusable Payment Codes (BIP47).
Both used together with a lightweight client which does not leak crucial information (so not using electrum for example) but a wallet implementing Block filters (e.g. Wasabi) your privacy can be significantly increased.
Whether that is enough for you, depends on your definition of
privacy. You won't get anonymity tho.