Would the wife be sinful if she deleted bad Bluetooth clips from her husband’s phone, despite his forbidding her from doing so, or is it obligatory for her to delete them?

Spying and tracking the private affairs of Muslims is forbidden, based on the Almighty's saying: "And do not spy," and the Prophet's (peace be upon him) saying: "Indeed, if you follow the private affairs of people, you will corrupt them or be close to corrupting them."

Therefore, it is not permissible for you to spy on your husband. However, if you come across forbidden things without spying, you must advise him and remind him of Allah gently, and ask him to remove them. If he does not respond, then there is no blame upon you for deleting and destroying them; rather, it is obligatory if you are able to do so and are safe from harm, for the Prophet (peace be upon him) said: "Whoever among you sees an evil, let him change it with his hand; if he cannot, then with his tongue; if he cannot, then with his heart."

If you fear that changing it by hand will lead to a great tribulation, then this change is dropped, and changing with the tongue and heart remains.