The comprehension of the structural behavior of historical buildings is pivotal for preserving them through suitable interventions and designing adequate monitoring systems. The complexity lies in articulated geometries, poor knowledge of materials, and often unknown construction sequences, which may have influenced the stress field in a non-linear material such as masonry. This paper addresses the issues through different modeling strategies accounting for material uncertainties in a probabilistic framework that leverages sensitivity analyses on Finite Element (FE) global models. The prior probability density functions of soil and masonry mechanical parameters are chosen based on expert judgment and available data from experimental campaigns. Response surfaces surrogate numerical models based on general Polynomial Chaos Expansion (gPCE), thus turning burdensome runs into faster analytical evaluations. Modal analyses on the entire FE model of the Baptistery of Pisa are performed to evaluate the sensitivity of masonry and soil mechanical parameters on the variation of the first modal eigenvalues. This aims at understanding the minimum recognizable parameter variation when monitoring natural frequencies, thus guiding the sensors' best positioning.