For example, in case you have an amount of 0.0009BTC in two different wallets, the best(only) option is to first consolidate and combine them into one wallet and after that send as much as you want to the mixer.
Correct me if I am wrong, if I have UTXOs of 0.0009 BTC in and 0.0005 BTC in an address and then decided to mix them. This should be fine, the output will be more than the minimum with some change if I am to spend exactly 0.001 BTC in the mixer's deposit address. There's no need to first consolidate.
Consolidating beforehand is not necessary but if the UTXOs are in different wallets they will need to move them to the same wallet first so they can deposit in a single transaction. Depositing them in separate transactions would probably not be valid because then people could just spam many small deposits that add up to 0.001 BTC and burden them with high fees.