It is safe. XMR.TO is very well established in the community and nobody can link your XMR wallet to your BTC address.

It is not like exchanging BTC with ETH through an exchange where everyone is capable of linking every address to a wallet and every wallet to a real person, since Monero's blockchain is obfuscated. Senders are protected through Ring Signatures where 10 different people sign a transaction with you and make you anonymous within a group of signers.