Mithril does not specifically say it can negate movement speed penalities by medium armor. It mentions specific mechanics and statistical changes, but never says that movement speed change. Merely treating medium armor as light armor does not do this because the movement speed penalties are traits of specific armors, not to light and medium armors as a whole. A FAQ even mentions that considering one armor as a different type doesn't change the statistics.
But many people argue that medium mithril armor doesn't impede your speed?
Yes, it is one category lighter for the purposes of move speed. So Medium becomes Light for the purposes of move speed.
The FAQ was specifically addressing the "other limitations" section not the "movement" section. Basically, there was a question as to what kinds of "other limitations" applied.
Basically, does a magic enhancement that requires medium armor work with Medium Mithral (that counts as light) or does it need Heavy Mithral (that counts as medium)? The answer is whatever the type was before Mithral is factored in (ie Medium).
Mithral: Mithral is a very rare silvery, glistening metal that is lighter than steel but just as hard. When worked like steel, it becomes a wonderful material from which to create armor, and is occasionally used for other items as well. Most mithral armors are one category lighter than normal for purposes of movement and other limitations. Heavy armors are treated as medium, and medium armors are treated as light, but light armors are still treated as light. This decrease does not apply to prof iciency in wearing the armor. A character wearing mithral full plate must be prof icient in wearing heavy armor to avoid adding the armor’s check penalty to all his attack rolls and skill checks that involve moving. Spell failure chances for armors and shields made from mithral are decreased by 10%, maximum Dexterity bonuses are increased by 2, and armor check penalties are decreased by 3 (to a minimum of 0).
Is celestial armor like this too? It doesnt mention movement.
You, mithral has been a staple material since 3.x to let you move full speed. That's how it is. Why do people need to sift through a thousand rules on a subject literally the majority of people agree does a specific thing. If you're looking for specifics I am not your dude. But yo, if everyone pretty much agrees on it, it's probably in the rules somewhere. But I'm pretty sure if you treat it as light armor then it doesn't.
I never played 3.5e so...
This bright silver or gold +3 chainmail is so fine and light that it can be worn under normal clothing without betraying its presence. It has a maximum Dexterity bonus of +8, an armor check penalty of –2, and an arcane spell failure chance of 15%. It is considered light armor and allows the wearer to use fly on command (as the spell) once per day.
It is Light Armor, it does not need such a statement.