What is the ruling on visiting websites to use something permissible or impermissible, knowing that the visit increases their income and that they contain matters of disbelief? And is visiting them considered participating with them in their acts of disbelief?

There is no objection to entering websites that offer permissible benefits for a legitimate purpose. The visitor is not considered a participant in any idolatrous matters contained therein, as long as he does not endorse them. It is preferable to limit oneself to Islamic websites. As for using them for a forbidden matter, it is prohibited, whether the websites belong to disbelievers or Muslims.