It takes one OPSEC slip up for someone to link a wallet address to you. So yes, your transactions being public doesn't matter as long as you are cognizant of that 24/7 365 days a year.

You can resolve this issue by repeatedly tumbling your money, using the same tumbling scheme as everyone else. This will reduce the value of your wallet slightly, to pay the mining fees, but it's… hm. That sounds equivalent to inflation or tax, except that the lost money doesn't go towards anything useful: it just goes towards buying ASICs and burning electricity.

That is unfortunately a fairly weak form of anonymity. With a fully public network you can trace even the most meticulously tumbled and laundered tokens. And while they may not exclusively trace back to you, they'll trace into a mixer and out of a mixer with a large majority of the inputs and outputs being tainted.

Most exchanges, etc won't really touch accounts or UTxO that are messing with mixers.

Because of that it's generally just better to use "properly" private and anonymous blockchains instead. If they are fully opaque then tracing becomes effectively impossible.