Is Anarchism Utopian?

Depends on the definition, if anarchism is defined from the etymology of anarchy or chaos, then it is not even utopian but dystopian.

Let us do away with ideology first and deal with facts.

If anarchism is defined as statelessness, then the utopian claim is false, for one simple reason: the origin of human society had been WITHOUT the  state.

Human society emerged from the prehistoric stateless hunter-gatherer societal relationship

Notes the Wikipeida.org (bold mine)

Hunting and gathering was the ancestral subsistence mode of Homo. As The Cambridge Encyclopedia of Hunter-Gatherers says: "Hunting and gathering was humanity's first and most successful adaptation, occupying at least 90 percent of human history. Until 12,000 years ago, all humans lived this way." 

What characterizes the hunter gatherer societies?

From another Wikipedia.org article (bold mine)

Hunter-gatherers move around constantly in search of food. As a result, they do not build permanent villages or create a wide variety of artifacts, and usually only form small groups such as bands and tribes. However, some hunting and gathering societies in areas with abundant resources (such as the Tlingit) lived in larger groups and formed complex hierarchical social structures such as chiefdoms. The need for mobility also limits the size of these societies. They generally consist of fewer than 60 people and rarely exceed 100. Statuses within the tribe are relatively equal, and decisions are reached through general agreement. The ties that bind the tribe are more complex than those of the bands.Leadership is personal—charismatic—and used for special purposes only in tribal society. There are no political offices containing real power, and a chief is merely a person of influence, a sort of adviser; therefore, tribal consolidations for collective action are not governmental. The family forms the main social unit, with most societal members being related by birth or marriage. This type of organization requires the family to carry out most social functions, including production and education.

In other words, 90% of human history has been about tribal anarchism.

The origin of the government came during the transition from hunter-gatherer to the agricultural age or the evolution towards pastoral societies.

Pastoralism is a slightly more efficient form of subsistence. Rather than searching for food on a daily basis, members of a pastoral society rely on domesticated herd animals to meet their food needs. Pastoralists live a nomadic life, moving their herds from one pasture to another. Because their food supply is far more reliable, pastoral societies can support larger populations. Since there are food surpluses, fewer people are needed to produce food. As a result, the division of labor (the specialization by individuals or groups in the performance of specific economic activities) becomes more complex. For example, some people become craftworkers, producing tools, weapons, and jewelry. The production of goods encourages trade. This trade helps to create inequality, as some families acquire more goods than others do. These families often gain power through their increased wealth. The passing on of property from one generation to another helps to centralize wealth and power. Over time emerge hereditary chieftainships, the typical form of government in pastoral societies.

From the above account the protection of private property played a significant role in ushering the state.

There are modern day examples of stateless tribal anarchist societies, Somalia—until recently before the  forced introduction of government through the intervention of the US government—and Southeast Asia’s Zomia.

Now let us inject the ideological philosophical component of anarchist societies. 

According to the Wikipedia.org there are several schools of thought, mutualism, individualist anarchism and social anarchism (which is broken down into collectivist anarchism, anarcho-communism, anarcho-syndicalism).

There are even several offspring of ideological anarchism. The internet seems like an example of crypto-anarchism.

As to whether these ideological anarchism are utopian or not is beyond the scope of this post.

The bottom line is that anarchism as defined by statelessness has been an integral part of human society. They are anything but utopian.