What is the ruling on participating with a friend who will take out a loan to complete a project, and is it permissible for me to accept this partnership?

It is impermissible to partner with someone who offers an usurious loan, because that constitutes aiding him in sin. Allah has commanded cooperation in righteousness and piety, and forbidden cooperation in sin and aggression. If you do not partner with him, he would not be compelled to take the forbidden usurious loan. And everything intended for the unlawful or leading to sin is forbidden.