Adi Shankara is the upholder of Advaita (Non-dual) philosophy. There is popular belief among Advaitins that one shouldn't differentiate between Gods as they all are same. But is this thing explicitly told by Adi Shankara in his works? Also what is the reason to consider that all deities are same?
Adi Shankaracharya in the Bhasya of Brihadaranyaka Upanishad 1.4.6 states:
यथेयं श्रुतिर्व्यवस्थिता तथा प्रजापतिरेव सर्वे देवा इति निश्चितोऽर्थः। स्रष्टुरनन्यत्वात्सृष्टानाम्, प्रजापतिनैव तु सृष्टत्वाद्देवानाम् । अथैवं प्रकरणार्थे व्यवस्थिते तत्स्तुत्यभिप्रायेणाविद्वन्मतान्तरनिन्दोपन्यासः, अन्यनिन्दानाय स्तुतये। तत्तत्र कर्मप्रकरणे केवलयाज्ञिका यागकाले यदिदं वच आहुः- 'अमुमग्निं यजामुमिन्द्रं यज' इत्यादि --- नामशस्त्रस्तोत्रकर्मादिभिन्नत्वाभिन्नमेवाग्न्यादिदेवमेकैकंमन्यमाना आहुरित्यभिप्रायः । तन्न तथा विद्यात्, यस्मादेतस्यैव प्रजापतेः सा विसृष्टिर्देवभेदः सर्व एष उ ह्योव प्रजापतिरेव प्राणः सर्वे देवाः ।
Just as told in this Shruti; by that Prajapati himself is form of all Gods (prajApatirEva sarvE devA) the direct meaning of this is because manifestation is indifferent from manifestor and Prajapati has created all Gods. Now, this being the import of the section, the views of some ignorant people are being put forward as a eulogy on that. The criticism (nindA) of one serves as a praise (stutI) to another. When, in discussing ceremonials, the priests, who know only mechanical rites, talk of particular gods, saying at the time of performing a sacrifice, 'Sacrifice to Agni,' .'Sacrifice to the Indra,' and so on, thinking, on account of differences regarding name, type of hymns recited or sung, function, and the like, that they are separate gods, it should not be understood that way, because these different Gods are projection of Prajapati himself, for Prajapati in Prana form is all Gods (prajApatirEva prAna: sarvE devA).
The last line 'Prajapati in Prana form is all Gods' is of significant importance because it's fully described in Prashna Upanishad where there is Prana Stuti. One such verse is:
इन्द्रस्त्वं प्राण तेजसा रुद्रोऽसि परिरक्षिता ।
त्वमन्तरिक्षे चरसि सूर्यस्त्वं ज्योतिषां पतिः ॥ ९ ॥
Indra thou art, O Prana, and Rudra, too, in prowess. Thou art the Protector. Thou movest in the sky; thou art the sun, the lord of lights.
Adi Shankara commentary on this is as:
किंच, इन्द्रः परमेश्वरः त्वं हे प्राण, तेजसा वीर्येण रुद्रोऽसि संहरन् जगत् । स्थितौ च परि समन्तात् रक्षिता पालयिता ; परिरक्षिता त्वमेव जगतः सौम्येन रूपेण । त्वम् अन्तरिक्षे अजस्रं चरसि उदयास्तमयाभ्यां सूर्यः त्वमेव च सर्वेषां ज्योतिषां पतिः ॥
Further, O Prana, you are Indra, the Supreme Lord. By valour you are Rudra, engaged in destroying the world. Again, during the time of the existence of the universe, you, in your benign aspect, are the preserver (of the universe) on every side. You move for ever in the sky by rising and setting. You are the sun, the lord of all the luminaries.
Thus it is clear that Prana itself is in the form of Gods like Indra, Destroyer Rudra, Protector (Vishnu), Sun etc...
Thus as a final conclusion we have:
1) Lord Prajapati himself is in the form of all Gods ( prajApatirEva sarvE devA).
2) Manifested things are non different from manifestor thus all Gods should be regarded as same.
3) Prajapati through Prana Form, manifests himself as different gods like Indra, Agni, Rudra, Vishnu, Surya, etc... Thus they are all one same God.
4) Owing to the difference in names, use of different hymns and rituals, the Gods shouldn't be regarded different because all Gods are projection of Prajapati himself.