If you know the mass and radius of the object, you can calculate the tidal force. (You can map this with a gravity sensor on a probe or just throwing a bunch of rocks through the system and watching how it bends their trajectories)
Then it depends on the spacecraft. If your ship is 1 km long and made of cotton candy, then it won't take much force at all to destroy it. If it's 10 m long (dramatically reducing the tidal effect) and made of solid diamond then it can fly much closer. Not that there would be anything to see.
Read Neutron Star by Larry Niven (1966) for a dramatic description of a close flyby of a compact stellar mass object.
> If you know the mass and radius of the object, you can calculate the tidal force.
The issue is more the position of the object. Good luck doing trajectory correction for an object you can't see.
The "throw a bunch of rocks" technique might help, but since they'd be unpowered they're not going to be following a trajectory that minimizes tidal force. It's still going to be enormously difficult to thread the needle through an invisible object that's going to tear you apart if you're not on the right trajectory.
Perhaps the technique Beowulf Shaeffer used could work if it were done with instruments - measure the tidal forces aboard the ship and navigate accordingly to minimize them.
How would you figure out the safe trajectory to avoid tidal forces?