So I am making a D-Day game based off of Call of Duty: WW2. Every time a player gets a certain amount of points they get a new rank, and they're character loads back up. Why does this not work? Can you fix my script?

game.Players.PlayerAdded:Connect(function(plr)
	
	local char = plr.Character
	
	local leaderstats = Instance.new('Folder')
	leaderstats.Name = 'leaderstats'
	leaderstats.Parent = plr
	
	local rank = Instance.new('StringValue')
	rank.Name = 'Rank'
	rank.Value = 'Private'
	rank.Parent = leaderstats
	
	local points = Instance.new('IntValue')
	points.Name = 'XP'
	points.Value = 0
	points.Parent = leaderstats
	
	while true do
		
		wait(1)
		points.Value = points.Value + 10
		
	end
	
	if (points.Value >= 50) then
		
		rank.Value = 'Private First Class'
		char:LoadCharacter()
		
	end
	
	if (points.Value >= 100) then
		
		rank.Value = 'Private Second Class'
		char:LoadCharacter()
		
	end
	
end)

The while loop acts like a wall to code under it, but not in it.

In line 19-24, you have a while loop going on. Since your condition is constant and you never specified a terminating condition, the loop is infinite. Thus, everything at line 26-38 will not execute.

You should instead listen for the Instance.Changed event. It fires when a property of an instance changes. For ValueBase objects (StringValue, IntValue, ect), the Changed event is modified to fire only on the Value property change.

local Players = game:GetService('Players')

Players.PlayerAdded:Connect(function(client)
	local leaderstats = Instance.new('Folder')
	leaderstats.Name = 'leaderstats'
	leaderstats.Parent = client
	
	local rank = Instance.new('StringValue')
	rank.Name = 'Rank'
	rank.Value = 'Private'
	rank.Parent = leaderstats
	
	local xp = Instance.new('IntValue')
	xp.Name = 'XP'
	xp.Value = 0
	xp.Parent = leaderstats

	xp.Changed:Connect(function(newXP)
		if (points.Value - 50 >= 0) then
			rank.Value = 'Private First Class'
			client:LoadCharacter()
		elseif (points.Value - 100 >= 0) then
        		rank.Value = 'Private Second Class'
			client:LoadCharacter()
		end
	end)
end)

while (true) do
	for _, client in ipairs(Players:GetPlayers()) do
		client.leaderstats.XP.Value = client.leaderstats.XP.Value + 10
	end
	wait(1)
end

Instead of multiple loops going on, why not just have one big loop?

Notice the better identifiers I used. Also, :LoadCharacter() is a member of the Player instance, not the character. Characters are just Models, if they had :LoadCharacter, then we'd be calling :LoadCharacter on buildings next thing