Great acharyas like Ramanujacharya have stated that Lord Narayana is the supreme being and other gods like Brahma and Shiva occupy subordinate positions. Yet many common people believe that all 3 gods in the trinity are the same. Do the vedas support such a position?
Not only 3 gods, but all gods and goddesses are the same. If you haven't already heard of the famous Rig Vedic verse 1.164.46:
इन्द्रं मित्रं वरुणमग्निमाहुरथो दिव्यः स सुपर्णो गरुत्मान् ।
एकं सद् विप्रा बहुधा वदन्त्यग्निं यमं मातरिश्वानमाहुः ॥
They call Agni as Indra, Mitra, Varuna, and the divine golden-feathered great being. The one reality Agni, the sages call variously, as Yama and Matarishva.
Also, the great Niruktakara Yaskacharya says (7.4):
माहाभाग्याद् देवताया एक आत्मा बहुधा स्तूयते । एकस्यात्मनोऽन्ये देवाः प्रत्यङ्गानि भवन्ति । ... इतरेतरजन्मानो भवन्ति । इतरेतरप्रकृतयः । कर्मजन्मानः । आत्मजन्मानः । ... आत्मा सर्वं देवस्य ।
Due to the majesty of the deity, one Atman is praised in many ways. Of the one Atman, the many deities are limbs... They are born from one another. They have each other's nature. They are born because of their specific function. They are born from the Atman. The Atman is the all-in-all of the deity.