2 weeks in India

Do you have a religion in particular? Or, what exactly do you mean by "history of religion"? If you want a mix, Amritsar (Sikhism), Ajmer (Islam), and Varanasi (Hinduism and Buddhism) would give you plenty of flavour, though you'd have to travel quite a lot. Also some time in Delhi, where there is more history than anywhere else in India. The Nizammuddin neighborhood of Delhi could certainly do as a substitute for Ajmer. And there are many other religions represented in Delhi as well.

The Taj Mahal is sublime. But only go there if you have a particular interest in seeing it. There are also fabulous monuments of the same era in Delhi - the Red Fort, and the old city's Jama Masjid, for example.

Question - how necessary is the Taj Mahal?

Nothing is necessary. However, if you are going to be in the neighbourhood, seeing the real thing in situ blows away every photograph or moving image of the Taj you have ever seen.

And, of course, Agra has many buildings worth visiting beyong the Taj; and two or three essential day trips.

https://www.lonelyplanet.com/india/agra/attractions/agra-fort/a/poi-sig/449177/356509
https://www.lonelyplanet.com/india/agra/attractions/itimad-ud-daulah/a/poi-sig/449183/356509
https://www.lonelyplanet.com/india/agra/attractions/jehangirs-palace/a/poi-sig/1324905/356509

https://www.lonelyplanet.com/india/uttar-pradesh/fatehpur-sikri
https://www.lonelyplanet.com/india/uttar-pradesh/mathura
https://www.lonelyplanet.com/india/uttar-pradesh/vrindavan

I am sad to have to miss out on Ajanta/Ellora caves but i understand its just not logistically possible in only 2 weeks.

It's a matter of priority. Ajanta and Ellora would mean a day flying to Aurangabad; a day for Ellora and a day for Ajanta; and then flying out of Aurangabad the next day. You have to give up something else to fit that time commitment.

My main interest is history and religion

For history, it's pretty difficult to beat Delhi. But equally Jaipur (with three forts and India's first planned city) has its share of history, and does Agra; and Varanasi is plain old. If you're inclined to ruins and deserted citadels, then Hampi. Mandu. Nalanda. Sanchi. Fatehpur Sikri. (and Delhi).

Religion is everywhere in India - it's unavoidable. If it's temples you want, then almost anywhere in the State of Tamil Nadu. Plus: Jaisalmer, Ranakpur, Mt Abu. Amritsar. Khujaraho. Ajanta and Ellora. Delhi.

Of historical religious significance:

Sarnath (easy day trip from Varanasi)
https://www.lonelyplanet.com/india/uttar-pradesh/sarnath

Bodhygaya
https://www.lonelyplanet.com/india/bihar-and-jharkhand/bodhgaya

Bhopal (for Sanchi)
https://www.lonelyplanet.com/india/madhya-pradesh-and-chhattisgarh/sanchi

(in which case, add Bhimbetka: https://www.lonelyplanet.com/india/madhya-pradesh-and-chhattisgarh/bhimbetka)

Nalanda
https://www.lonelyplanet.com/india/nalanda

Broader destinations of a religious bent:

Buddhism:
The Buddhist Circuit is usually regarded as: Sarnath / Bodhgaya / Kushinagar +Lumbini which is in Nepal.
Dharmasala

Hinduism:
The Seven Ancient Towns: Ayodhya; Mathura; Haridwar; Varanasi; Kanchipuram; Dvaraka; Ujjain
The Four Holy Dhamas: Puri (East); Rameshvaram (South); Dvaraka (West); Badrinatha (North)
The Four Maha Kumbha Mela Sites: Prayaga ( Allahabad); Haridwar; Ujjain; Nasik
The Chota Char Dham: Yamunotri, Gangotri, Kedarnath, Badrinath.

Sikhs:
Golden Temple in Amritsar. Damdama Sahib, situated in the village of Talwandi Sabo near Bhatinda. Keshgarh Sahib situated at Anandpur. Hazur Sahib is on the banks of Godavari in Maharashtra. Patna Sahib is situated in Patna the capital of Bihar.

Jains:
Ranakpur, Rajasthan; Dilwara (Mt Abu), Rajasthan; Girnar, Gujarat; Palitana, Gujarat; Patna, Bihar; Sammet Shikhar (Peak of Wisdom), Bihar; Sravanabelagola, near Bangalore.

Muslims:
Mecca Masjid, Hyderabad
Jama Masjid, Delhi
Nizamuddin Dargah, Delhi
Tomb of Salim Chishti, Fatehpur Sikri
Haji Ali Dargah, Mumbai
Ajmer Sharif Dargah, Ajmer
Dargah Hazratbal, Jammu & Kashmir

That's a lot of places you have there in your list for 2 weeks. While the places are good, going from A to B is going to take a lot of time. In case you chose to visit Rishikesh to explore yoga and mountains, I recommend joining a 2-day retreat. I recommend because it will cover stay, meals, and also introduce you to yoga and spirituality. I participated in one few weeks ago and totally loved it. Check out the retreat details over here.
Good luck with your travel.
Travel tip - narrow down your list so that you make the most of places you plan on visiting.

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