I've done nothing with traveling setting to setting, and actually find the multiverse idea distasteful, almost repugnant.
1. I exclusively run homebrew settings. They often have their own cosmology and pantheons. The concept that "D&D requires" that it's actually connected to everything - or even anything - else is a hard NO. You don't get to dictate my world like that. You most especially don't get to set player expectations such that they think anything from across the multiverse should be allowed to exist.
2. I strongly dislike "kitchen sink" settings when I play. Warforged in Eberron have a strong and dynamic place in the setting. They are connected to the history, and their existing in meaningful to what what and what is, forcing changes on the world. Warforged in FR are "oh look, mechanical men" with all serial numbers filed off.
3. Related to both number one and two, I enjoy flavorful settings. Dark Sun during the default age shouldn't have divine options available for PCs. Eberron is cut off from anywhere except the few specific planes occasionally because of the Ring of Siberys. Don't try to take away their uniqueness by connecting them up to a multiverse which will actively damage them by changing core assumptions of the settings.
Again, this is the idea of a multiverse - there being multiple planes in the cosmology is just fine. And that could include multiple material planes - if that's what that setting sets up. I had such in my Errantas setting that I ran multiple campaigns in. There were material planes accessible through the various elemental planes, and most of the races on the starting plane were refuges brought there by various deities to escape disasters or genocide because the walls of this particular material plane were "thin" and it was not too hard to get people here. But that doesn't mean that others of those material planes were FR, or that they could worship Tempus or meet Mordinkainen plane hopping. There were actually 18 "mantles" for gods, and the various pantheons filled most of them with Ascended from each culture. We also had strong genius loci (gods of places), and fisher-king like "the king is the land and the land is the king" connections to it. Other pantheon not part of that just didn't exist anywhere in (or connected to!) that setting.