Xjyuk

I feel that Scout against Pyro is perhaps the most difficult confrontation between classes. Scout has the lowest amount of health in the game (alongside Engineer, Sniper and Spy) and Pyro's flamethrower can kill him nearly instantly. Close encounters must be avoided, making shotguns far less useful. I can only see some items such as Shortstop and Mad Milk changing the situation. Jumping around with related items (Winger, Atomizer) equipped may be viable, but experienced Pyro players should be able to take the Scout down as the flamethrower doesn't demand accurate aim.

Is it recommended to avoid direct confrontations with Pyro entirely?

UPDATE: This question was written before a major update:

• 
  

  Flamethrowers were able to do full damage regardless of the spread of
  their flames, rewarding maximizing flame spread over focusing on a
  target. We've made changes geared toward preserving the current damage
  range of flamethrowers, but requiring better aim to do so.

  
  
  
  • Flame damage per second now ramps up based on density of flame encountered, up to 200%
  
  
  • Initial flame damage per second reduced by 50%, resulting in the max damage being unchanged
  
  

You don"t need to avoid contact. In my experience an experienced scout can more often than not defeat an experienced pyro.

The best "tool" that a Scout has to use to his advantage is his movement speed.

Under most circumstances, the Scout can move faster than the Pyro, and the scattergun can be used right outside the Pyro's attack range, so as long as you remain moving you are harder to hit therefore harder to take damage. Obviously you cannot get too close as the Pyro is a very good DPS class at close range, so just stay close without being too close.

Your pistol can also play a vital role, allowing you to pepper the Pyro with a few shots at medium range, which the Pyro is very weak at.

Some unlocks that can help aid you include the Sun-on-a-Stick with its fire resistance should you catch on fire and need to temporarily retreat, the Mad Milk can be used for extinguishing yourself, or perhaps even the Force-a-Nature with its knockback ability keeping the Pyro away from you.

I have two load outs in mind
if your just trying to survive an encounter
Primary: the Force-a-nature
secondary: the pretty boys pocket pistol
melee: the sun a stick
Reasons why:
why you would want the force a nature is because of its insane knock back to keep the Pyro away from you so you only have to only worry about after burn also the sun on a stick because it gives you a 25% fire resistance then after you have used those weapons to get away from the Pyro use the mad milk to extinguish any after burn.

I hope this helped, I will make a second answer about how to attack a pyro as scout.