One airdrop has been asking me to cash out the tokens using my TON wallet, but when I try to, the prompt I receive is that I do not have TON to complete the transaction. Must I have TON to receive Telegram-based airdrops?
This happened because you didn't have enough Toncoin in your wallet that you would have used to pay for the transaction fee to claim your airdrop token. Yes, for you to claim your airdrop token, you need to fund your wallet with the required Toncoin the Ton blockchain wants as a fee before you can be able to claim your airdrop token. You can buy Toncoin on any centralized exchange where Toncoin is listed, withdraw the Toncoin from the centralized exchange to the wallet you want to use, and claim the airdrop token. You will spend less money on the fee because the Ton blockchain fee is low.