So this means that at the moment the best non-custodial wallet where we can store most of our coins is trust wallet as it supports almost all of the blockchains.
You've got Coinomi as well, but I'd personally stick to TrustWallet especially if you're interested in using DEXes that uses WalletConnect.
All these support usdt (TRC20) :
Atomic wallet
Guarda Wallet
exodus.com
Coinomi
Jaxx Liberty
Trustwallet sounds very convenient .....but how to use it privately and sudo-anonymously - is that really impossible ??