Native acceptance, and why it is the weakest of the four.
Anubis is one of the few markets of this kind that takes Ethereum without converting it behind the scenes. That is worth understanding, and so is the cost.
Most markets listing Ethereum are running a conversion service that swaps it on arrival. You pay the bridge spread and the swap itself becomes a recorded event. Native acceptance means the market issues an Ethereum deposit address and watches the chain directly, which is the only version worth caring about.
Bitcoin and Litecoin move discrete outputs, so a careful user gets a fresh receiving address each time. Ethereum works on accounts: one address holds a balance and every transaction it has ever made hangs off the same identifier. Address reuse is the default rather than a mistake.
The consequence is that an address which once received an exchange withdrawal carries that association into everything it does afterwards, including this payment. Using an address that has done nothing else is the minimum, and it is still a permanently readable record.
Ethereum fees move with network demand and can spike sharply within an hour. Check the current estimate rather than assuming, because a figure that was reasonable this morning may not be now.
Most Ethereum wallets are browser extensions, and installing extensions into Tor Browser makes it more distinguishable and adds code with access to what you are doing. Use a standalone application, keep it separate from the browser you reach the market with, and copy the deposit address across by hand. Do not weaken the browser to accommodate a wallet.
When you already hold Ethereum, the alternative is paying a swap fee, and you have accepted that the payment is permanently readable. Choosing it from scratch on privacy grounds is not defensible.