What is the ruling on purchasing from a brand that belongs to a company which produces another brand that carries a sacred word, "such as the Messiah," on its packaging designed for disrespectful disposal, and is this considered direct cooperation in sin?

It is obligatory to respect papers or containers upon which the name of Allah the Almighty or the names of prophets and angels are written, and it is not permissible to degrade them. Buying permissible goods from a company does not cause harm even if the company uses its money in haram (unlawful) ways, as there is no sin upon the buyer. This is supported by the fact that the Prophet, peace be upon him, and the Companions used to buy from and deal with Jews without asking about the sources of their money or how they spent it, as long as the commodity was permissible and there was no direct intention to aid in sin. Commercial dealings with someone who uses their money in haram fall under the category of indirect and unintended assistance, which is permissible. A company that writes the name of Christ believing in his divinity is promoting a disbelieving slogan, and this is forbidden for them, but buying from them is permissible for the consumer.