It will be a mistake for you to consider Hanuman as a monkey or as any other being.
We have different classes of beings in Hinduism like - Deva (divine beings), Rishi (Seers, the celestial beings), MAnava (human beings) and Pashu Yonis (animals, birds etc).
And, among these categories, Hanuman belongs to the Deva category.
From, Tantra SArah's Hanumata Kalpa section, we get the following dialogue between Goddess PArvati and Lord Shiva:
ShaivAni gAnapatyAni shAkAni vaishnavAni cha |
saurAni chAnyAni yAni tAni cha ||
ShrutAni tAni devesha tvad
vaktrAni nihsritAni cha |
Kinchitdanyattu devAnAm sAdhanam
yadi kathyatAm ||
Goddess says - O Deveswara, I have heard from you the procedures of
various Sadhanas -- like those related to Shiva, to Ganapaty, to
Shakti, to Vishnu and to Surya. Now, I want to hear the procedures of
SAdhanas of various other deities.
Point to note is Goddess is asking for procedures of worship for anya devA-s i.e. for other deities.
To this request, Lord Shiva replies thus:
Srinu devi pravakshyAmi sAvadhAnAva dhArraya |
punyam mahApAtak nAshanam ...
O Goddess, I will reveal the procedure of Hanumatkalpa, please listen
carefully. This practice is the giver of great merits and the destroyer
of great sins..
So, this shows that Hanuman is a DevatA in Hinduism.
One mantra for him is "Ham pavan nandanAya swAha", which mentions him as the son of the Vedic deity VAyu.
So, the rules like "Sudras can not recite Vedas etc" are not applicable here as we are talking about a god.