This paper presents a study carried out in the Italian region of Umbria, after the 2016 Central Italy earthquake. The aim is to address the problem of the conservation and protection of architectural heritage in Italy. The application of retrofitting strategies, while improving the seismic performance of historic—and frequently listed by conservation bodies—buildings, will not significantly alter their appearance, will be reversible, and fall within the principle of minimum intervention (minimal (least) intervention (or conservative repair)). These issues were evaluated in the paper by considering the different points of view of structural engineers and conservators. Heavy structural-oriented interventions as well as the underestimation of the importance of the structural safety for masonry monuments has produced, in the past, irreversible damage to important buildings and monuments, and loss of architectural heritage in Italy. The requirement of structural safety, especially for monuments located in seismic-prone areas, is compared with the need for conservation. The Italian building guidelines for interventions of cultural heritage are also discussed, highlighting some limitations and important advancements.