Acne in ancient civilizations is something that has likely never been studied in depth, but I believe we can draw conclusions about the prevalence of acne back then based on the causes of acne today.

Much of the following is going to be quoted from this source, with others being attached.

In westernized societies, acne is a nearly universal skins disease afflicting 79%-95% of the adolescent population. Epidemiologial evidence suggests that acne incidence rates are considerably lower in nonwesternized societies. In 2002 a study (linked earlier) was published investigating the occurance of acne of the Kitavan Islanders of Papua New Guinea and the Aché hunter-gatherers of Paraguay. Of the 1200 Kitavan subjects (300 of which aged 15-25 years) no case of acne was observed. Of the 115 Aché subjects (15 aged 15-25 years), no case of active acne was observed.

So it would seem clear that there is a pretty massive difference in the rate of acne occurance between these people and the people of the United States, among other modernized societies. One that this research team concludes cannot be attributed to genetic differences but likely results from differing environmental factors. What factors, you ask?

For the next couple of paragraphs I'd like to make the connection between the diets of westernized societies and these virtually acne free populations.

Insulinlike growth factor 1 (IGF-1) and insulin has an inverse relationship with serum SHBG. Let me define those for you.

IGF-1 is a potent mitogen (encourages cell division) for virtually all body tissues ^source.

Serum SHBG (sex hormone binding globulin) reduces the amount of androgens circulating to tissues. IGF-1 and insulin inhibit the synthesis of SHBG, thereby increasing the bioavailability of these androgens. Androgens stimulate sebum production, which as we know, is essential to the development of acne.

Insulin creation is your bodies response to high blood sugar levels. Unfortunately, sebum production is stimulated by insulin ^source as well as IGF-1, through androgens.

The diets of western societies are much different to the diets of these Aché and Kitavan people in that their diets are composed of minimally processed plant and animal foods, and are virtually devoid of typical western carbohydrates that yield high glycemic loads that may acutely or chronically ELEVATE INSULIN LEVELS. Cue the chain reaction that I attempted to spell out with the previously mentioned relationships between insulin, IGF-1 and SHBG. Recently acculturated hunter-gatherer populations who have adopted western diets frequently are hyperinsulemic (high insulin levels in relation to the amount of glucose in your body), whereas less westernized populations rarely exhibit these symptoms

I didn't forget about IGF-1. Where can you find copious amounts of IGF-1 in western diets? Dairy. Milk in particular contains IGF-1, which as I mentioned before has the ability to increase levels of circulating androgens. In two large cross-sectional studies, milk consumption was positively associated with higher plasma IGF-1 levels ^source. Recent studies have suggested that this increase in the IGF-1 stimulus to acnegenesis may be mediated by a hyperinsulunemic response to the ingestion of fluid milk ^source.

I'd like to add that hyperinsulinemia is also the root cause of some other fun diseases like type 2 diabetes, dyslipidemia, coronary artery disease, and obesity.

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Back to the original question posed by the OP. What was acne like back in ancient times, or even 300 years ago? The answer to that question lies mostly in their diet. Here are some examples of populations where acne is a virtually unknown disease. Acne was almost certainly less common back then.

Prior to World War II, Okinawa was an isolated island outpost in the South China Sea, and its native inhabitants lived a rural life with few or none of the trappings of industrialized societies. Extensive medical questionnaires by US physicians administered to local physicians who had practiced from 8 to 41 years revealed that these people had no acne vulgaris.

Here is a video regarding the traditional Okinawa diet & its health benefits.

Dermatological examination of 9955 schoolchildren (aged 6-16 years) conducted in a rural region in Brazil found that only 2.7% of this pediatric population had acne. Dermatological examination of 2214 Peruvian adolescents by pediatricians demonstrated that acne prevalence (grades 1-4) was lower (28%) in Peruvian Indians than in mestizos (43%) or whites (45%).

In South Africa, dermatologists found lower rates of acne among the Bantu than among whites residing in Pretoria. Bantu adolescents (aged 15-19 years; n = 510) maintained a 16% incidence rate of acne, whereas among the white adolescents (n = 1822), the incidence was 45%. For the entire sample of Bantus of all ages (n = 3905), the overall occurrence of acne was 2%, whereas in the total white sample across all ages (n = 16 676), the incidence of acne was 10%. Among the Zulu it was suggested that acne became a problem only when these people moved from rural African villages to cities. All of these studies suggest that the prevalence of acne is lower among rural, nonwesternized people than in fully modernized Western societies.

And as I referred to earlier:

Of 1200 Kitavan subjects examined (including 300 aged 15-25 years), no case of acne (grade 1 with multiple comedones or grades 2-4) was observed.

Tubers, fruit, fish, and coconut represent the dietary mainstays in Kitava. Dietary habits are virtually uninfluenced by Western foods in most households. The intake of dairy products, alcohol, coffee, and tea was close to nil, and that of oils, margarine, cereals, sugar, and salt was negligible. Estimated carbohydrate intake was high, almost 70% of daily energy, while total fat intake was low (20% of daily energy). Virtually all of the dietary carbohydrate intake was in the form of low–glycemic load tubers, fruits, and vegetables.

Of 115 Aché subjects examined (including 15 aged 15-25 years) over 843 days, no case of active acne (grades 1-4) was observed.

The Aché diet contains wild, foraged foods, locally cultivated foods, and Western foods obtained from external sources. By energy, their diet consists of 69% cultigens, 17% wild game, 8% Western foods, 3% domestic meat, and 3% collected forest products.25,26 The cultigens consist mainly of sweet manioc, followed by peanuts, maize, and rice, whereas the Western goods are mainly pasta, flour, sugar, yerba tea, and bread.23

As a second question: we know now that stress and other factors can cause acne, not just cleanliness. Was this realized in the past and we're people treated for their acne, or was it just sort of accepted as a part of life?