Using Bitcoin to buy legal products is completely legal. Research peptides are legal to buy and possess in the US (they're sold as "not for human consumption" research chemicals). The payment method doesn't change the legality of the underlying purchase.
That said, cryptocurrency transactions are not anonymous despite popular belief. Bitcoin is pseudonymous — transactions are recorded on a public blockchain. If you purchase BTC on a KYC exchange (Coinbase, etc.) and send it directly to a merchant, there's a clear trail linking your identity to the purchase. This is fine for legal purchases but worth understanding.
If privacy is a specific concern, that's a separate discussion (see the Monero/Lightning thread). But for most people making straightforward peptide purchases, basic Bitcoin is perfectly adequate and the 10-15% discount is worth the minor hassle of setting up a wallet.