This is primarily a question of what constitutes nonmagical restraints, as per the definition of Freedom of Movement.

Freedom of Movement:

You touch a willing creature. For the duration, the target’s movement is unaffected by Difficult Terrain, and spells and other magical effects can neither reduce the target’s Speed nor cause the target to have the Paralyzed or Restrained conditions. The target also has a Swim Speed equal to its Speed.

In addition, the target can spend 5 feet of movement to automatically escape from nonmagical restraints, such as manacles or a creature imposing the Grappled condition on it.

Using a Higher-Level Spell Slot. You can target one additional creature for each spell slot level above 4.

The spell points out normal manacles, and a grappling creature, as forms of nonmagical restraints. But doesn't provide examples of magical restraints. If a magical restraint is any restraining item that is enchanted, and thus a magic item, then wouldn't a Rope of Mending, if used as a rope to restrain someone, be considered a magical restraint?

Here is the definition of a Rope for 2024:

Rope

As a Utilize action, you can tie a knot with Rope if you succeed on a DC 10 Dexterity (Sleight of Hand) check. The Rope can be burst with a successful DC 20 Strength (Athletics) check.

You can bind an unwilling creature with the Rope only if the creature has the Grappled, Incapacitated, or Restrained condition. If the creature’s legs are bound, the creature has the Restrained condition until it escapes. Escaping the Rope requires the creature to make a successful DC 15 Dexterity (Acrobatics) check as an action.

I am not hopefully that the release of the 2024 DMG will provide any clarity on something potentially as niche as this, though I'd image that the Rope of Mending may be described as being able to do anything a rope can do, in addition to Mending itself.


Edited for spelling.

I'd agree that it's unclear, though personally I would not rule that a Rope of Mending is a magical restraint. While it is a magic item, its magical properties cannot be used to restrain someone, so that isn't a magical restraint. Magical restraint would be something like the Entangle spell, or the magic item Dimensional Shackles.

Quote from wagnarokkr >>

I'd agree that it's unclear, though personally I would not rule that a Rope of Mending is a magical restraint. While it is a magic item, its magical properties cannot be used to restrain someone, so that isn't a magical restraint. Magical restraint would be something like the Entangle spell, or the magic item Dimensional Shackles.

 
A rather reasonable ruling: that the restraining effect must be magical. That, while a Rope of Mending is a magical item, the restraining effect is still mundane. Thus, it is still subject to the effects of Freedom of Movement.

 I agree with you. I'd rule the same for this interaction.