I tried the 'Clamped' option and for some odd reason was unsuccessful....so I created this script. I hope it'll help those who are also in the same position as me.

#if UNITY_EDITOR && UNITY_5_6
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEditor;
using UnityEngine.UI;

public class ScrollRectNANEditor : EditorWindow
{
static ScrollRectNANEditor _window;

[MenuItem("ScrollRect (5.6) Bug Fixer/Open Window #F9")]
public static void Open()
{
if (_window != null)
EditorWindow.GetWindow<ScrollRectNANEditor>().Close();
//Show existing window instance. If one doesn't exist, make one.
_window = EditorWindow.GetWindow<ScrollRectNANEditor>("", true, typeof(SceneView)) as ScrollRectNANEditor;
}

[MenuItem("ScrollRect (5.6) Bug Fixer/Fix Now")]
public static void LaunchBootScreen()
{
Open();
_window.FixBug();
}

void OnGUI()
{
if (GUILayout.Button ("Fix Now", EditorStyles.toolbarButton))
FixBug();
}

void FixBug()
{
ScrollRect[] scrolls = FindObjectsOfType(typeof(ScrollRect)) as ScrollRect[];
for (int i = 0; i < scrolls.Length; i++)
{
ScrollRect scroll = scrolls[i];
scroll.enabled = false;
}

for (int i = 0; i < scrolls.Length; i++)
{
ScrollRect scroll = scrolls[i];
if (scroll.movementType == ScrollRect.MovementType.Clamped)
{
scroll.movementType = ScrollRect.MovementType.Elastic;
scroll.elasticity = 0;
}
if (scroll.content != null)
{
scroll.content.anchoredPosition = FixIfNaN(scroll.content.anchoredPosition);
}
}

for (int i = 0; i < scrolls.Length; i++)
{
ScrollRect scroll = scrolls[i];
scroll.enabled = true;
}

_window.ShowNotification(new GUIContent(scrolls.Length + " instances have been successfully fixed ;)"));
}

Vector2 FixIfNaN(Vector2 v)
{
v.x = v.x.FixIfNaN();
v.y = v.y.FixIfNaN();
return v;
}

Vector3 FixIfNaN(Vector3 v)
{
v.x = v.x.FixIfNaN();
v.y = v.y.FixIfNaN();
v.z = v.z.FixIfNaN();
return v;
}
}
#endif

Thank you, PhaneV. Changing from clamped to elastic solved it.

This happens to me in the current version 5.6.0f3.
The solution to avoid this till they fix this bug is the one that PHANEV said:

This issue stopped reproducing after I changed the Movement Type of the scroll rect to "Elastic". Was previously using "Clamped".

We are having the same problem, scroll rect value goes to NAN when we move it. In 5.6.0f3

So is there gonna be a fix for 5.6 too or will this be only fixed in 2017? o.O

Really messes up our UI in 5.6f3

Further on:
This issue stopped reproducing after I changed the Movement Type of the scroll rect to "Elastic". Was previously using "Clamped".

I tried this after finding this bug here, which might be related (?) :
https://issuetracker.unity3d.com/issues/rect-transform-values-are-set-to-nan-when-decreasing-the-height-of-the-content-game-object-in-scroll-view

Happens in 5.6.0f2 Personal.
Thanks @ Egproject, otherwise I would've updated to try on it too.

The issue is still present in 5.6.0f3 Plus. All my drop downs got broken with the update, unfortunately. Scroll rect still unusable unless ready to redo it 100 times until you get lucky.

Reproduces with 5.6.0f3 Personal