There have been overall shifts, but there is also a "horizontal" diversity in the approach taken by historians, based on different theoretical models. Today, almost any good academic history will contain a section discussing its methodology. Academic history essentially consists of writing narratives which are then critiqued, rejected, amended and so forth in the broader historiographical discussion.

One broad shift that I always think of is from the Rankean paradigm of figuring out history "as it really was" based on identifying the most reliable sources or harmonizing diverging narratives. This kind of presupposes that a history should always represent what a historian think is, overall, the most plausible account of everything. The problem is that this generally leads to a prohibitively broad scope (or more likely, vastly suboptimal criteria for choosing how to read sources), and therefore, historians will often deliberately write histories from a particular perspective. For example, Richard Payne's "A State of Mixture: Christians, Zoroastrians and Iranian Political Culture in Late Antiquity" re-examines the notion of the zealous, theocratic Sasanians oppressing their Christian and Jewish minorities by reading the traditional Armenian and Aramaic martyrdoms as situated in an Iranian political context, and discussing how the Sasanian Empire could be understood as a pluralistic society under a supreme monarch, submission to whom was paramount. For instance, this perspective suggests that Khusrau II's pilfering of the True Cross from Jerusalem was not merely intended to humiliate his Christian adversaries, but also to yield a glorious trophy for his Christian subjects and a banner for his legitimacy among the Christians of the Eastern Mediterranean he intended to subjugate.

This reading has various advantages, such as highlighting potential tensions between a more pluralistic monarch and religiously conservative high nobility and clergy, and yielding a potential explanation of the dissolution of noble support for Khusrau at the zenith of his empire's power. But it isn't necessarily the most plausible or palatable narrative in all regards - it has a tendency to gloss over real religious violence and persecutions as a necessity to uphold the barriers Payne takes as essential to this "state of mixture". However, Payne's monograph is far more useful in this form as a point of reference, than would be the likely outcome of an attempt to consider every possible angle and implication of every single source to highlight every single possible implication of interest.

So yes, the era a history is written in should absolutely be taken into account, but writing will differ not just based on time but also on the individual historian and their preferences, whether they have a degree in history or something like philology, and so forth. Ultimately, you should look at the historian's argument for reading a source in a particular way, as well as why what that reading yields might be interestikng. In most cases, you are unlikely to find a single monograph that is a truly satisfactory account of an era; studying the actual historiography and differences between accounts is necessary to get a strong understanding.