The individual soul is embodied since time immemorial. It is very difficult for him to simply theoretically understand that he is not the body. Therefore, the bhakti-yogī accepts the Deity of Kṛṣṇa as worshipable because there is some bodily conception fixed in the mind, which can thus be applied. Of course, worship of the Supreme Personality of Godhead in His form within the temple is not idol worship. There is evidence in the Vedic literature that worship may be saguṇa or nirguṇa—of the Supreme possessing or not possessing attributes. Worship of the Deity in the temple is saguṇa worship, for the Lord is represented by material qualities. But the form of the Lord, though represented by material qualities such as stone, wood or oil paint, is not actually material. That is the absolute nature of the Supreme Lord.
(Bhagavad-Gita----12:5----purport).

The Lord being kaivalya (one alone), there is no matter in Him. He is one without a second, and therefore the Almighty Lord can appear in any form without being contaminated by the material conception. Therefore, festivities in the temple of the Lord, as held generally, are like festivals performed during the manifestive days of the Lord of Dvārakā, about five thousand years ago. The authorized ācāryas, who know the science perfectly, install such temples of the Lord under regulative principles just to offer facilities to the common man, but persons who are less intelligent, without being conversant with the science, mistake this great attempt to be idol worship and poke their nose into that to which they have no access. Therefore, the ladies or men who observe festivals in the temples of the Lord just to have a look at the transcendental form are a thousand times more glorious than those who are nonbelievers in the transcendental form of the Lord.
(Srimad Bhagavatam----1:11:24----purport).

Here in this verse, it is definitely assured that the Supreme Lord is not impersonal. He is a person, but His body is different from those of conditioned persons like us. Otherwise, meditation beginning from the praṇava (oṁkāra) up to the limbs of the personal body of Viṣṇu would not have been recommended by Śukadeva Gosvāmī for the attainment of complete spiritual perfection. The Viṣṇu forms of worship in great temples of India are not, therefore, arrangements of idol worship, as they are wrongly interpreted to be by a class of men with a poor fund of knowledge; rather, they are different spiritual centers of meditation on the transcendental limbs of the body of Viṣṇu. The worshipable Deity in the temple of Viṣṇu is identical with Lord Viṣṇu by the inconceivable potency of the Lord.
(Srimad Bhagavatam----2:1:19----purport).

Māyāvādīs and atheists accept the forms of the Deities in the temple of the Lord as idols, but devotees do not worship idols. They directly worship the Personality of Godhead in His arcā incarnation. Arcā refers to the form which we can worship in our present condition.
(Srimad Bhagavatam----3:25:35----purport).

"If one offers Me with love and devotion a leaf, a flower, fruit or water, I will accept it." The devotee offers eatables in the form of vegetables, fruits, leaves and water to the arcā-vigraha. The Lord, being bhakta-vatsala, compassionate upon His devotees, accepts these offerings. Atheists may think that the devotees are engaged in idol worship, but the fact is different. Janārdana, the Supreme Lord, accepts bhāva, the attitude of service. The neophyte devotee engaged in the worship of the Lord may not understand the value of such worship, but the Supreme Lord, being bhakta-vatsala, accepts His devotee and in due course of time takes him home.
(Srimad Bhagavatam----4:30:28----purport).

Even logically we can understand that all material elements are expansions of the energy of the Lord. Since the energy of the Supreme Personality of Godhead is nondifferent from His personal body, the Lord is always present in His energy, and He manifests Himself on account of the ardent desire of a devotee. Since the Lord is supremely powerful, it is logical that He can manifest Himself in His energy. Deity worship or worship of the śālagrāma-śilā is not idol worship. The Deity of the Lord in the house of a pure devotee can act exactly as He can in His original transcendental personality.
(Sri Caitanya Caritamrta----1:14:9----purport).