Is celibacy intrinsic to Buddhism?

Something which is intrinsic to Buddhism applies to it regardless of its levels of practice or cultural variation. Insofar as the 8-Fold Path is definitive for Buddhism as a stipulated formula of practical application interpreted according to insight received in meditation, there is no part of it which clearly requires celibacy.

It would be far more helpful to talk about monasticism, the extremes to which it tends to aim, and whether celibacy is intrinsic to Buddhist monasticism, or indeed monasticism of every other kind. The justification for it being essential and important to monasticism is in part what also sets up the contextual Indian framework of the Four Stages of Life (Student, Householder, Forest-Dweller, and Renunciate): that the energetic focus and interest wanes from or turns aside from conventions, reproduction, and the drama of emotional co-dependence, and shifts toward cohabited placidness, the peace attractive to those with spiritual values, and the equipoise available to those set upon Nirvana.

Originally, in the 1st sermon, it was made quite clear the Noble Eightfold Path was a celibate path.

Thus have I heard. On one occasion the Blessed One was dwelling at Baraṇasi in the Deer Park at Isipatana. There the Blessed One addressed the bhikkhus of the group of five thus:

Bhikkhus, these two extremes should not be followed by one who has gone forth into homelessness. What two? The pursuit of sensual happiness in sensual pleasures, which is low, vulgar, the way of worldlings, ignoble, unbeneficial; and the pursuit of self-mortification, which is painful, ignoble, unbeneficial. Without veering towards either of these extremes, the Tathagata has awakened to the middle way, which gives rise to vision, which gives rise to knowledge, which leads to peace, to direct knowledge, to enlightenment, to Nibbāna.

And what, bhikkhus, is that middle way awakened to by the Tathagata, which gives rise to vision … which leads to Nibbāna? It is this Noble Eightfold Path; that is, right view, right intention, right speech, right action, right livelihood, right effort, right mindfulness, right concentration. This, bhikkhus, is that middle way awakened to by the Tathagata, which gives rise to vision, which gives rise to knowledge, which leads to peace, to direct knowledge, to enlightenment, to Nibbāna.

SN 56.11

It would be ideal if a question like this were framed as either an inquiry into personal experiences and views or as relating specifically to the precepts of specific schools of Buddhism.

am not able to make out if celibacy is a must for Buddhists?

The answer I would give is no. Only one Buddhist ever was required to practice celibacy: that was Shakyamuni; and he required it of himself by "marrying himself to the Earth." In an allegorical sense this marriage is indicated by the story of Shakyamuni's final struggle with Mara (the devilish nature of delusion integral to all beings; an innate part of consciousness); when challenged by Mara to produce any person who could testify that he, Shakyamuni, was qualified to become the Tathagata, the Teacher to all living beings, Shakyamuni placed his hand, palm upon the ground and said "The Earth is my witness" (it is said that when he did this, the ground trembled in many directions, scattering the followers of Mara, who fled in terror).

Vinaya, the codified rules of monastic conduct, do not apply outside the school which claims them. So the Vinaya of Theravadan Buddhists cannot be applied to those answering from a Mahayana perspective (as informed readers will no doubt deduce that I am).

I have been celibate for more than a dozen years as I write this. I am in my 50s and am a male American person. It has some great aspects. However, everything is like a blade that has two edges.

a delicious cake is displayed in a cake shop showcase and a male and female ,both are tempted to eat it .they go inside, order it, eat it together with joy. now nobody will think it as immoral,etc etc. There is no guilt associated with it. but as regards to sensuality ,eating is attached with guilt,immorality etc etc. It is this attached guilt is hindrance in any kind of spirituality be it hinduism,buddhism,christianity,islam and lot many. this associated taboo has its roots in the early primordial humans living in tribes,groups. The desire of sensual pleasure makes the women vulnerable and vica versa .to protect it the taboo might have been got associated. we cannot help it now ,since this taboo is coming from thousands of years . even the small children are taught to refrain from touching their private parts and hence how they will also come out of this taboo. the cycle goes on repeating . the taboo is not associated with wearing nice clothes,eating delicious food,enjoying good movie. if the guilt of being immoral is absent then there is no need to give so much importance to this taboo. whole religions are whirling on this aspect only. so listening/following to those are also filled with ego of maintaining celibacy .On the contrary the ego or "i " is to dissolved,ruptured. So it is upto the individual what to follow. celibacy making the "i' still stronger or tabooless,guiltless non celibacy.

If you choose a way of a monk - you have to keep your vows so celibacy is a must for you.

If you choose to be a lay Buddhist, you should undertake 5 precepts and one of those is avoiding sexual misconduct. When two people love and respect each other they can generate lots of happiness through sex. In tantric Buddhism giving sexual pleasure is actually seen as a form of generosity.

One of the most important practices in Vajrayana Buddhism is meditating on Yidams (Buddha forms). Some of the forms represent male and female Buddhas in union. If Buddhas do it, there must be nothing intrinsically impure in sex.