Broadly, they did not.

Religions were typically amalgamated, incorporated, or adapted into the Roman pantheon. Examples of amalgamation and incorporation include Sulis, in Bath, England, a famous example. She was the goddess of the springs there, and roughly analogous to Minerva, alongside a host of other deities from Gallic Britain. This is not particularly unusual, and the temple in Bath is dedicated to Sulis-Minerva (famously examined by Cunliffe in 1966). This is a process known as syncretism.

They were also sometimes brought wholesale into the Roman religious system - Isaeum, Serapeum, Temples of Attis and Cybele, these temples all existed in Rome and all served non-traditional, or non-Roman deities. By which I mean, not of the pantheon we have come to know and love. Roman concepts of religious identity appear to be very fluid. It is only when we come across monotheistic cultures that there is a challenge. In a polytheistic system, everyone can have different gods, we can all be chill, and religion toddles along. In a monotheistic system, someone has to be right, and everyone else is wrong.

All that being said, there are instances of religious outrage, although these are often after the conquest begins. For example, in Lucan's account of the Gallic Wars, Caesar comes across a grove outside Marseilles, with altars dripping in human gore (Bell. Civ. 3.399-452). Human sacrifice is, in Roman, terms, a no no. Like, a big one. So the priests are evil etc etc, yadda yadda yadda, Caesar chops down the grove personally, but is still a bit ambiguous in doing so. However, this is a poem, written years after the events, and is not to be taken as fact. The grove probably never existed. What it does illustrate is a trope, of religion being used as a marker for a dichotomous moral judgement. Which is a fancy way of saying: human sacrifice bad; animal sacrifice good. Therefore you bad because you religion bad.