Do the scriptures mandate that devotees need to have idols and portraits of gods in their houses?
Well I don't think there is any mandate as such but yes there are certain rituals and practices stated in our scriptures that one should follow religiously when they worship a deity in the form of an image or idol.
A little info as stated here about : Idol Worship/Murti Puja
An idol or an image is a living embodiment (arca) of God. It is not a lifeless form. Life is poured into every image or idol when it is reverentially worshiped with devotion. Devotion has such power. According to our Puranas, with devotion you can awaken the divine power which is hidden in any object. By overcoming the duality of the subject and the object or the knower and the known you can experience oneness with the divinity who is present in all things.
Now read here about the correct way of doing deity worship:
SB 11.27: Lord Kṛṣṇa’s Instructions on the Process of Deity Worship:
The details of the worshiping process are as follows: The devotee should bathe both physically and by chanting mantras, and then he should perform the utterance of Gāyatrī at the prescribed juncture of the day. He should arrange a seat facing either east or north, or else directly facing the Deity, and should bathe and clean the Deity. Then he should present clothing and ornaments, sprinkle water on the vessels and other paraphernalia to be used in the worship, and offer water for bathing the Deity’s feet, arghya, water for washing His mouth, fragrant oils, incense, lamps, flowers and food preparations. After this, one should worship the Lord’s personal servants and bodyguards, His consort energies, and the spiritual masters by chanting their respective mūla-mantras. The worshiper should recite prayers from the Purāṇas and other sources, offer obeisances flat on the ground, beg for benediction, and place on himself the remnants of the Lord’s garlands.
So if you think you can follow the exact rituals daily without any excuses then you should probably have them at home but otherwise it would be recommended to visit a temple, simply read the following explanation by Sadhguru about temples and their importance:
The temple was not created as a place of God or a place of prayer. It was created as a place of energy where everyone could go and make use of it.
Temples in India, were built as a very deep science. They were not created for worship. When I say temple, I am referring to the ancient temples. Most modern temples are built just the way you build shopping complexes. Temple building is a very deep science. If the basic aspects of the temple – the size and shape of the idol, the mudra that the idol holds, the parikrama, the garbha griha, and the mantras used to consecrate the idol are properly matched, a powerful energy system is created.
Bottom line: Idol worship is neither mandatory nor prohibited in Hindu religion.