My view (not an expert) is, 'don't let perfect become the enemy of progress'.
If you are now, or think you are likely to be in real danger then this does NOT apply to you. You need to look at something like cash exchange in a public space (but take steps to maintain your anonimty) or I've also heard of pple using amazon gift cards to obscure then linknfrom you fiat to btc)

TL;DR 
using a non custdial P2P, which doesn't ask for ID, is alrleady moving the needle a long way in the right direction for your privacy. Don't sweat about which fiat to use, unless you're a human rights activist in danger or someone with a target on their back (in which case, I'm not qualified to advise you, but tools exist to help - if you have time, try lookng here https://my.cracktheorange.com/).

extended ramblings...
 
For everyone else, the point is to make it much harder for governments (& criminals) to track what we do with our money, particularly how much fiat we convert into hard money. Sure, they could look at my bank statements, and try to identify which transfers are to peers in (allegedly) exchange for btc. They'd have to go through these (receiving fiat bank) accounts, one by one. High volume P2P vendors will probably be known but, as time goes on, & if more peers use P2P to exchange into/out of btc, this becomes harder for agencies to work through. If you do something to justify the effort to analyse all you fiat TXs, then they will do that. BUT this is very different from being able to effortlessly inspect every spend and receive in your fiat account, and use algorithms to categorise us by whatever metrics they consider relevant for control and supervision of 'the peasants' (us).

So use whatever fiat is easy for you, and for which you can find a peer to match your exchange need (buy/sell). With challenger banks (e.g. Revolut) it's easy to switch fiat into whichever flavour of weak money you need to complete the exchange.  Buy 'little' (below your banks 'fraud protection' threshold, you can find this out by trial and error - start with say < $200 - 300  & see if they call to ask 'Are you sure?', or askNostr) & often. 
It's like how inoculation against polio / measles etc works, we're building up resistance of the herd until it's not practical to mass-surveil.

Hope that helps.