All players get hat even though its only for players with a 1?

This is because you left the two if statements at lines 5 and 25 completely separate. This means if a player has a value of 1, they would get their hat removed then get the accessory. However, because the hat part of the script is outside of the value, anyone can get it. Try this: ->

game.Players.PlayerAdded:connect(function(player)
    player.CharacterAdded:connect(function(character)
        if player:WaitForChild("leaderstats").Money.Value>= 1 then -- "If they have money value"
            wait(0.1)
            local d = character:GetChildren()
            for i=1, #d do
                if (d[i].className == "Accessory") then
                    d[i]:remove()
                end
            end
            if character:findFirstChild("Humanoid") ~= nil then -- Accessory script
                local h = Instance.new("Accessory")
                local p = Instance.new("Part")
                h.Name = "Hat"
                p.Parent = h
                p.Position = character:findFirstChild("Head").Position
                p.Name = "Handle"
                p.formFactor = 0
                p.Size = Vector3.new(-0,-0,-1)
                p.BottomSurface = 0
                p.TopSurface = 0
                p.Locked = true
                script.Parent.AfroMesh:Clone().Parent = p
                h.Parent = character
                print("It should work")
                h.AttachmentPos = Vector3.new(0, -0.20, 0)
                wait(.1)
            end
        end --Skipped over people without value
    end)
end)