In a word no. People in the past certainly did not accept damp and mold as the norm, at least not if they could afford to. The way modern buildings and traditional buildings deal with moisture is fundamentally different.*

Modern buildings are typically built to be fully waterproof. In the UK, where I am, most houses built within the last 100 or so years are typically built with cavity brick and/or cement block walls built over a damp proof membrane (DPM). The DPM stops damp rising through the foundations to the walls, whilst the cavity in the wall stops moisture from rain penetrating through the wall. Modern buildings are also typically built with cement based mortar (and often render) and gypsum plaster, all of which are waterproof.

Traditional buildings were typically built with no damp proof membrane, and the wall materials (earth, stone, brick or timber, held together with lime or earth mortars) are highly vapour permeable. This means that moisture from the ground wicks up through the walls and then evaporates out of them. The walls will also absorb and release moisture from the air, maintaining a fairly stable humidity. Rain water might also soak somewhat into the walls, and then evaporate when it's sunny.

Traditional buildings (actually all buildings) also need good ventilation to stay healthy and comfortable. The commonest and simplest form is cross-ventilation, ie. having windows on opposite sides of a building so that the pressure differential on either side will draw fresh air through the building. In 19th century Britain some of the poorest urban workers lived in 'back-to-back' houses, which had no cross-ventilation and were considered insanitary as a result. They were mostly demolished when local board's of health got the powers to condemn the substandard buildings.

The result of all this is that traditional buildings (when well maintained) tend to buffer humidity quite well, and feel very comfortable.

Modern, waterproof buildings will often trap the moisture you produce** inside them and require more ventilation which usually ends up being mechanical.

Most basements of course have inadequate ventilation, and often sit below the water table so they are prone to damp problems. Historically it was usually just a fact of life that cellars were often a bit damp, but this was usually mitigated by the permeable nature of the building's fabric and natural ventilation, so that whilst you might not want to sleep down there, they were good for storing food.

It's also worth noting that every building is different, and the complex relationship between the way it's built and the way it is situated in its environment has a big impact on how it deals with moisture.

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*When I say modern and traditional, this varies by region and by country. Where I live in the UK the cut off point is generally given as around 1919.

** Humans produce a lot of moisture in buildings. Washing, cooking, drying clothes and even breathing produce a lot of moisture.