You're redefining the term to fit with your insistence that theism is inherently a religion.
I think that theism clearly is a religious belief. (Actually a vague category of religious belief, but you know what I mean.)
That doesn't mean that it's "a religion", in the sense that it's a socially established system of group religious belief and practice.
To be a religion, it requires more than just beliefs and theology.
Then what should we make of the many millions of people whose religiosity is highly individual and unique to them?
Specific practices, typically including codes of behaviour and how to conduct oneself in society, are just as key to defining a religion. And certain ones emphasise practices much moreso than the 'beliefs' end of it.
Yeah, it's true. Most of the world's socially established religious traditions are probably closer to orthopraxies (right-practice) than orthodoxies (right-belief). Most group-religiosity seems more concerned that prescribed practices are performed (sacrifices, public prayers, ritual acts...) than that members all believe specified doctrines inside their own heads. Christianity, especially its Protestant variety, is kind of atypical in that regard.
There are plenty of religions out there whose practices and beliefs are not to the exclusion of other ones. There are some that are framed with the idea in mind that one can practise more than one simultaneously--or at least in parallel.
I think that when that happens, it's often a matter of specialization. For example, we often find Buddhism combined with other religious traditions in East Asia. A traditional Chinese would often be a Confucian when it came to social ethics, a Buddhist when it came to salvation, and a Daoist when it came to this-worldly fortune and magic. It isn't so much that the religions overlapped, but rather that each of them was supreme in its own sphere of life interest.
Greco-Roman-style polytheism was very inclusive in a different way. They accepted that there are lots of gods. Individual Greek city-states had patron gods or goddesses, and honoring that particular deity was as much a patriotic observance as a religious one. When ancient Greeks visited different cities, they would often pay honors to that city's deity, without any anxiety about practicing a foreign religion.
And when the ancient Romans, who had similar ideas and practices, spread their empire into places like Gaul, they had no problems at all in treating the Celtic gods and goddesses that people recognized there in the same way. These were just more gods that people worshipped in distant places, and no big deal at all. It wasn't seen as challenging or contradicting their own observances, and making an offering to a Celtic god wasn't an occasion for any kind of anxiety or crisis.
As time went on and many Romans settled in Roman Gaul, we see Roman religion and Celtic religion syncretizing. As Romans and Celts intermarried and their cultures blended, they started to imagine that they were all really worshipping the same gods and goddesses, just with different names and mythological stories attached in different places.