Early Buddhism unapologetically favoured homelessness / monasticism for those striving to Awaken. Relationships —not only with their web of obligations, incl. moral / ethical duties, but also with their entangled sources of peer-pressure toward the status quo— were seen as major distractions, hurdles, binds. The ‘renunciants’ very clearly renounce the ‘ordinary’ ways of life.
This is not to say that spiritual progress wasn't accessible to lay people though. Some lay followers are praised enough in some suttas for it to be ambiguous whether they've reached “the goal of holy life.” Such examples tend to be sought by modern “secular Buddhists”.
And even if one takes the monastic (self-serving) perspective that it's virtually (if not theoretically) impossible for lay people to fully Awaken, the orthodox Theravāda school makes it clear that it's possible:
the monastic code (Vinaya (Mahāvagga, first Khandaka —the admission to the Order of bhikkhus)) mentions Yasa as a lay person attaining enlightenment, who ordained shortly thereafter;
the commentaries mention a few others (Santati, Uggasena… but some always dispute what's not canonical per se);
the Milinda Pañha formalises this possibility by pretending that « if a layman attains arahantship, only two destinations await him: either he must enter the Order that very day or else he must attain parinibbàna » (other places suggest « within 7 days » rather than « that very day »). Of course, the answers on these points come from bhikkhu Nagasena, not the Buddha himself, and are therefore subject to contestation;
the existence of paccekabuddhas (“solitary buddhas”; ‘solitary’ as in isolated from Dhamma and sangha, they're not necessarily hermits) is acknowledged, and it is considered that these people awaken by seeing causality ‘directly’, not by living in accordance with the monastic code.
And while striving as if one's hair is on fire might be wholesome, in a context where rebirth is considered standard, maybe there's much arrogance in picking a spiritual path only if one can attain the highest fruit within this lifetime. After all, even monastics are few to attain arahantship in this life…
If we consider ‘lower’ attainments (let's say “undeniable progress” rather than “the end of the path” or “the crossing to the other shore”) then the mahāparinibbāna sutta (DN 16) mentions going to the town Nādika, in which « over 50 laymen have passed away having ended the five lower fetters. They’ve been reborn spontaneously, and will be extinguished there, not liable to return from that world [hence non-returners]. More than 90 laymen have passed away having ended three fetters, and weakened greed, hate, and delusion. They’re once-returners, who will come back to this world once only, then make an end of suffering. In excess of 500 laymen have passed away having ended three fetters. They’re stream-enterers, not liable to be reborn in the underworld, bound for awakening. » The sutta doesn't give the length of time it took to get so many disciples accounted for1; however that's for one ‘town’ alone, in rural India, 26 centuries ago… so it remains an impressive number anyway, strongly suggesting that the lower attainments for lay people perfectly are within reach.
In some suttas, lay teachers shine, notably Anāthapiṇḍika praised by the Buddha for defending the teaching against misrepresentation (kiṃdiṭṭhika sutta, AN 10.93) and Citta, a non-returner householder who taught the Dhamma even to monks (saṃyojana sutta, SN 41.1).
Even based on ‘the’ orthodox school which survived to this day, we have a list of ten fetters from the suttas, which basically states that one might still lead an householder's life (incl. moderate sensual desires) and attain once-returner (the gross sensual desires are abandoned)… According to the Abhidhamma, views, doubt, attachment to rites and rituals, jealousy and greed are relinquished by stream-enterers, but gross sensual desires and anger are only abandoned by once-returners —and relinquishing subtle desires will make one a non-returner…
So, letting go of the arrogance “I'm capable of full Awakening in this life”, householders or lay people can certainly progress on the Path, and reach very meaningful attainments.
After all, the eightfold path doesn't mention “right social status”… and “right livelihood” isn't reduced to monasticism… After all, the “four noble truths” do not distinguish lay vs. monastic…
And the intermediate step of once-returner is nothing to dismiss, anyway!
Later Buddhism very much promoted the ideal of Vimalakīrti, the central figure of the Vimalakīrti nirdeśa, and yet this ideal is much harder to reach that once-returner… so, while it might act as a source of inspiration, by all means, maybe the example given shouldn't be seen as a requirement or a necessity.
Many views / ideas, as well as many feelings, are considered as inescapable in Buddhism, in the sense that they're conditioned: they'll arise due to causes you cannot magically wave away. You don't choose if / when they arise: you're not their controller (and this is, in fact, at the heart of the teachings on self-less-ness).
The goal of Buddhism is to ‘liberate’ people, by getting them to learn how to stop perpetuating “mental constructs,” i.e. by preventing people from freezing the “happiness value” of objects, experiences and yourself… “Not freezing the happiness value of something” is utterly different from “being a stone feeling nothing!”
An Enlightened person still has experiences (incl. pleasurable experiences and others), still acts, still engages with reality: the key difference with others is in not letting the action be an automatic reaction, pre-programmed, based on some assessment of the present moment by projecting ‘lessons’ from a frozen, subjective, past experience (which was indeed not identical to the present situation).
Buddhism is often associated with “be present”; the message is “don't let the memories, tendencies, habits, fears, etc. –all based on the past— decide for you (i.e. don't let these blind you from what's different this time).”
Liberation in Buddhism is from your past, and from the perpetuation of your past. If one interprets the message as “forget happiness” then it should only be in the sense of stopping “seeking happiness according to a prejudiced concept of what this should/might be”: don't think of what happiness is, be happy as it comes!
Buddhism doesn't ask you to stop having feelings (of pleasure, or displeasure), you cannot do that! Buddhism only leads you not to react automatically to such feelings, it leads you not to automatically switch from “that's nice” to “I want more” to “I want to own,” or from “I want” to “I need.” Buddhism leads you to fully experience the “that's nice!”
In that sense, it is very modern and much needed in a society that can quickly go from “this ice-cream tastes nice” to “I need a ice-cream-maker at my place”… only to realise later that the pleasure of the initial ice-cream was also dependent on the sunshine, the nice breeze, the friends one was with, etc., and that the ice-cream-maker-at-home did not bring the happiness that was projected onto it initially!
Buddhism teaches you to perceive and enjoy all aspects of the experience (in the moment, not once it's gone and missing): not just the ice cream, but the friends too!