Answer
This is one of the greatest confusions among followers of Sanatan Dharma. For this reason, many scholars describe Hinduism as a "polytheistic" religion, where many gods and deities are worshipped.
Therefore, it is extremely important to resolve this question properly.
You know that Sanatan Dharma has many scriptures, and they often speak in different voices. However, if we must arrive at a final conclusion, then it is only proper to give primary importance to that scripture which is not merely the voice of a sage, saint, or philosopher, but the direct voice of God Himself. For while the knowledge of saints and sages may be profound, it can still be limited, whereas God is omniscient.
Such a scripture is the Bhagavad Gita. It should also be remembered that not every verse of the Gita is spoken directly by God. Only those verses spoken by Lord Krishna Himself may be regarded as the direct speech of the Divine.
According to the Gita, God is One alone. In His essential nature, He is the unmanifest, formless, attributeless Brahman. Yet, when creation manifests, that same Supreme Reality reveals Himself in personal form as Narayana or Vishnu. At times, He also incarnates in human form, such as Sri Rama and Sri Krishna.
Therefore, the unmanifest Brahman, Lord Vishnu, and the incarnations Sri Rama and Sri Krishna are not separate realities. They are different manifestations of the same Supreme Truth.
Should one not worship any other deity?
On this subject, the Gita is very clear. Lord Krishna says that those who seek fulfillment of worldly desires worship various deities, because such deities grant material results quickly:
Kāmais tais tair hṛta-jñānāḥ prapadyante 'nya-devatāḥ, taṁ taṁ niyamam āsthāya prakṛtyā niyatāḥ svayā.
And further He says:
Antavat tu phalaṁ teṣāṁ tad bhavaty alpa-medhasām, devān deva-yajo yānti mad-bhaktā yānti mām api.
That is, the fruits obtained through the worship of deities are temporary and perishable. The worshippers of deities attain the worlds of those deities, whereas My devotees attain Me.
The Lord clarifies the same point elsewhere:
Kāṅkṣantaḥ karmaṇāṁ siddhiṁ yajanta iha devatāḥ, kṣipraṁ hi mānuṣe loke siddhir bhavati karma-jā.
Meaning: those who desire success in worldly actions worship the deities, because material success comes quickly in the human world through such worship.
The implication is also this: deities often grant the fulfillment of desires without necessarily judging whether those desires will ultimately benefit or harm the devotee. But God sees with a far wider vision. He grants only that which is ultimately beneficial for both the individual and the world.
Why worship God instead of deities?
The answer is that all worldly pleasures are temporary. Eternal and everlasting happiness comes only through moksha, liberation from the cycle of rebirth. Lord Krishna says:
Mām upetya punar janma duḥkhālayam aśāśvatam, nāpnuvanti mahātmānaḥ saṁsiddhiṁ paramāṁ gatāḥ.
Meaning: having attained Me, the great souls do not return again to this temporary world, which is a dwelling place of suffering.
When the soul attains God, it becomes free from rebirth and reaches the Supreme Abode:
“Yad gatvā na nivartante tad dhāma paramaṁ mama.”
The necessity of exclusive devotion
Now the most important point is this: realization of God comes only through exclusive surrender. If the mind remains divided among many deities, then it cannot be called complete self-surrender. The Lord says:
Ananyāś cintayanto māṁ ye janāḥ paryupāsate, teṣāṁ nityābhiyuktānāṁ yoga-kṣemaṁ vahāmy aham.
Meaning: those who worship Me alone with undivided devotion, I Myself take care of their welfare and needs.
The difference between reverence and surrender
Now you may ask: if exclusive devotion is supreme, then why does the Gita speak about honoring gods, teachers, scholars, and the learned?
Deva-dvija-guru-prājña-pūjanaṁ śaucam ārjavam, brahmacaryam ahiṁsā ca śārīraṁ tapa ucyate.
Here it is necessary to understand the distinction between "pūjan" and "upāsanā." "Pūjan" means respect, honor, and reverence. "Upāsanā" means devotional self-surrender. One should certainly respect deities, teachers, scholars, and the wise. But one's complete inner surrender should belong only to the Supreme God.
Therefore, if according to tradition or social custom you respectfully bow before your family deity, village deity, Goddess Saraswati, or Goddess Durga, and offer flowers and leaves, there is no fault in it. It is an expression of reverence and cultural propriety.
However, to seek ultimate refuge in them, to make worldly demands from them, or to treat them as the highest spiritual destination, is not presented in the Gita as the supreme path.
An analogy to understand
A married man has a unique and exclusive loyalty toward his wife. This does not mean he insults or disrespects other women. He will still treat them respectfully and courteously. But emotional and marital surrender belongs only to his wife.
Similarly, once you have accepted God as your chosen Deity, whether in the form of Sri Rama, Sri Krishna, Lord Narayana, or the formless Brahman, then your complete inner surrender should belong to Him alone.
Respect other deities. Bow before them. Offer flowers if needed. But do not build relationships of desire and dependence upon them.
If you must pray to them, then pray like this: "May I receive unwavering devotion toward my Lord." That is enough. The rest of your genuine needs will be taken care of by God Himself. That is His promise.
The message of the Gita
Ultimately, the message of the Gita is this: There is only one Supreme God. Exclusive devotion to Him is the path to liberation. Respect all deities, but make the Supreme Lord alone your final refuge.