if statements are running for no reason?

This happens because .Text is a string and CurrentAmmo and MaxAmmo are IntValues or (NumberValues) meaning that their .Value are numbers. According to Lua, strings and numbers are never equivalent. Meanwhile, Roblox allows you to assign a number to .Text and it will perform tostring on the number automatically.

To fix the problem, you need to make sure to compare identical types. You can either call tostring on the numbers or tonumber on the strings. Comparing strings may be the better option:

local CurrentAmmo = script.Parent.CurrentAmmo
local MaxAmmo = script.Parent.MaxAmmo
local config = script.Parent.Parent.Parent.Parent.Backpack.AWP.Config

while true do
    if CurrentAmmo.Text ~= tostring(config.CurrentAmmo.Value) then
        CurrentAmmo.Text = config.CurrentAmmo.Value
        print("changed current ammo")
    end

    if MaxAmmo.Text ~= tostring(config.MaxAmmo.Value) then
        MaxAmmo.Text = config.MaxAmmo.Value
        print("changed max ammo")
    end
    wait()
end

Note that it is far better to listen to the .Changed event of those Values rather than using a loop:

local CurrentAmmo = script.Parent.CurrentAmmo
local MaxAmmo = script.Parent.MaxAmmo
local config = script.Parent.Parent.Parent.Parent.Backpack.AWP.Config

config.CurrentAmmo.Changed:Connect(function()
        CurrentAmmo.Text = config.CurrentAmmo.Value
end)
config.MaxAmmo.Changed:Connect(function()
        MaxAmmo.Text = config.MaxAmmo.Value
end)

Unlike the events, the loop will run even when you don't need it to, wasting processing time (although you wouldn't notice the difference in this case).