All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
What you mentioned in the question does not prevent a Muslim from benefiting from such websites. It is well-known that the Prophet, sallallaahu ‘alayhi wa sallam, and Muslims in Madeenah carried out transactions with the Jews although the Jews were severely hostile to Islam and the Prophet, sallallaahu ‘alayhi wa sallam, and even attempted to kill him, although Allaah The Exalted saved him from their evil schemes.
However, if Ahlul Hall wal 'Aqd (the main policy-makers) in the Muslim nation advised to boycott any given organization or institution that is hostile to Islam in order to bring about a certain benefit, then in this case Muslims should adhere to their advice and boycott it, and it may even be obligatory to do so. For more benefit, please refer to Fatwa 91149.
Allaah Knows best.