To expand on my comment, the 'egalitarian' part of the question has been mostly dealt with on hist.SE, and the answer depends on your definition of egalitarian as well as the hunter-gatherers involved. It is true in the sense that they are/were more egalitarian than most of the post-Neolithic societies, the agricultural revolution being usually regarded as the seed of common-place inequality (as we conceive it today) owing to social stratification and specialization, e.g.
In the largest study of its kind, the researchers saw disparities in wealth mount with the rise of agriculture, specifically the domestication of plants and large animals, and increased social organization.
Their findings, published this week in the journal Nature [...] gathered data from 63 archaeological sites or groups of sites. Comparing house sizes within each site, researchers assigned Gini coefficients, common measures of inequality developed more than a century ago by the Italian statistician and sociologist Corrado Gini. In theory, a country with complete wealth equality would have a Gini coefficient of 0, while a country with all the wealth concentrated in one household would get a 1.
The researchers found that hunter-gatherer societies typically had low wealth disparities, with a median Gini of .17. Their mobility would make it hard to accumulate wealth, let alone pass it on to subsequent generations. Horticulturalists -- small-scale, low-intensity farmers -- had a median Gini of .27. Larger scale agricultural societies had a media Gini of .35.
As for peaceful... likewise... it's a matter of degree. A quick search finds a 2016 article in The Atlantic "A Prehistoric Mass Grave Suggests Hunter-Gatherers Weren’t So Peaceful":
In a study published today in the journal Nature, a team of anthropologists describe a prehistoric mass grave whose inhabitants died a violent death, evidence that small-scale warfare was alive and well even among hunter-gatherer communities.
On the other hand, if one takes a larger sample in the account, e.g.
Although recent studies on the evolution of warfare have been based on various archaeological and ethnographic data, they have reported mixed results: it is unclear whether or not warfare among prehistoric hunter–gatherers was common enough to be a component of human nature and a selective pressure for the evolution of human behaviour. This paper reports the mortality attributable to violence, and the spatio-temporal pattern of violence thus shown among ancient hunter–gatherers using skeletal evidence in prehistoric Japan (the Jomon period: 13 000 cal BC–800 cal BC). Our results suggest that the mortality due to violence was low and spatio-temporally highly restricted in the Jomon period, which implies that violence including warfare in prehistoric Japan was not common.
As for the nature of violence in hunter-gatherer societies, a 2016 Biol. Lett. review summarizes it as
Warfare among hunter-gatherers or small-scale farmers generally follows a strikingly similar pattern given the wide-variety of cultural variation and ecological habitats humans inhabit. Similar to lethal intergroup aggression in chimpanzees, the most common type of attack among hunter-gatherers is the raid or surprise ambush. A group usually consisting of all men would set out seeking to attack a much smaller group or a lone individual (Gat, 1999). Raiders would attempt to have the element of surprise through attacking at dawn or by ambushing unsuspecting individuals and quickly retreating to safety. These raids were usually low-risk to the attackers, however, injuries sometimes occurred. Chagnon (2009) for example, systematically collected data on scores of raids among a group of lowland horticulturalists living in Venezuela and Brazil called the Yanomamö. He estimated that less than 5% of raids resulted in injuries to attackers, and deaths were very rare. Likewise, data from the Waorani, a lowland horticultural group from Ecuador, show low death rates for aggressors without a single fatality for an attacker (Beckerman et al., 2009). In rare cases, multiple raiders could be killed, usually due to the attacking party being detected before their attack giving the intended victims time to prepare (Wrangham and Glowacki,2012). Larger conflicts called “battles” also occurred between hunter-gatherer groups, though they were much more variable than raids depending on features such as geography and social organization. Battles usually consisted of similarly matched groups throwing spears or shooting arrows at each other from a distance and hostilities would cease after one or two casualties. Although battles most often only resulted in just a few injuries or deaths, they could turn into a massacre if one side were greatly outnumbered (Burch, 2005).
As a caveat to this last narrative/picture derived using modern proxies, Gómez et al., (Nature, 2016) find a substantial difference in lethal violence levels between pre-historical hunter-gatherer bands and contemporary hunter-gatherer societies:
lethal violence is common in present-day bands and tribes [...], possibly because
there are more detailed data on mortality from living people than from
archaeological records. Nevertheless, some authors suggest that the
level of lethal violence has increased in hunter–gatherers because they
now live in denser populations in which intergroup conflicts are more
likely, or because they have contacted colonial societies where warfare
or interpersonal violence is frequent.
