Does Vedic Hinduism exist today?
Hinduism is almost always Vedic, even if the customs, method of worship, etc. change. It is true that performance of Vedic Yajna, rituals, etc. have decreased, but that's only obvious for this age of Kali. However, this doesn't mean that Vedic traditions have been forgot. Veda mantras constitute three kandas or sections (kanda trayatmika veda). They are:
- Karma Kanda 2. Upasana Kanda and 3.Jnana Kanda
The yajna and rituals for various gods are basically part of Karma Kanda. The purva mimansa school of thought deals with the ritualistic karma kanda portion. So it is the following of karma kanda portion that has decreased because doing those correctly are difficult in this age of Kali.
But the jnana kanda portion generally contains the upanishdas upon which the uttara mimansa or Vedanta school of thought is based. And there are many Vedanta schools of thought starting from Advaita Vada of Adi Shankara to Achintya Bhedabheda Vada of Shri Chaitanya. Those schools of thought are still active today and hence they are following the teachings of Vedas as outlined by their respective Acharyas.
So in a nutshell, Vedas are still followed today in Hinduism, but the karma kanda rituals have reduced. Apart from the fact that doing them correctly fulfilling all their requirements is difficult today, performance of them leads only to heaven and doesn't give liberation. So because those Vedic rituals deal with the three modes of material nature, it is generally suggested to avoid them if one wants liberation:
trai-guṇya-viṣayā vedā nistrai-guṇyo bhavārjuna
nirdvandvo nitya-sattva-stho niryoga-kṣema ātmavān [BG - 2.45]
The Vedas deal mainly with the subject of the three modes of material nature. O Arjuna, become transcendental to these three modes. Be free from all dualities and from all anxieties for gain and safety, and be established in the self.
But one may ask, if this is so then why does the Vedas contain those things? So the Bhagavatam says:
phala-śrutir iyaṁ nṝṇāṁ na śreyo rocanaṁ param
śreyo-vivakṣayā proktaṁ yathā bhaiṣajya-rocanam [SB - 11.21.23]
Those statements of scripture promising fruitive rewards do not prescribe the ultimate good for men but are merely enticements for executing beneficial religious duties, like promises of candy spoken to induce a child to take beneficial medicine.
We also know that how in Satya Yuga mode of attaining God was meditation and later on it become Yajna and worships in Treta Yuga and now in this age of kali, because people are not spiritually advanced and interested, remembering and taking of God's names is suggested in scriptures. Also following puranas makes Hinduism Vedic because purana and itihasa have been accepted as the 5th Veda (itihāsapurāṇaḥ pañcamo vedānāṃ - Chg. Up. - 7.1.4). Also in many rituals prescribed by the puranas, mantras of the Vedas are used. So regardless of whether we are following the puranas or the rituals of the Vedas, the core of Hinduism is still and will always be Vedic.
Now regarding the agnihotra and Yajnas, the followers of arya samaj possibly do agnihotra daily and I have heard there is a Gayatri Pariwar community who perform Yajna daily. Also from time to time many different organisations organise and perform Yajnas which are basically based on the karma kanda rules of Vedas.
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