To be fair, though, cash is anonymous by default, so I think that a replacement for cash should also be anonymous by default. Not saying that fiat is food, just my two cents.
Check out The Art of Invisibility by Kevin Mitnick.
Eliminate your low hanging fruit, the data that you give away freely without realizing it. There are many guides on how to use Bitcoin while maintaining your privacy, like https://bitcoiner.guide/privacy/
You strengthen your security bit by bit using the techniques that best align with your goals and your lifestyle. There are common best practices, but you have to examine your own weaknesses to find out what to work on first.
Discussion
I've only really been talking about on-chain Bitcoin. Layer 2 Lightning and layer 3 ecash build out privacy and anonymity by sacrificing security and censorship resistance.
A fedimint or cashu mint are anonymous and private by default, and those will probably end up being the primary method for payments with Bitcoin in the future.