Definition in opposition
A counter religion is defined in opposition to another, pre-existing natural religion (though they may falsely claim to be the “original”). This opposition is a core part of a counter religion, and not incidental.
So, we have the first two of the 10 commandments, combined with universalism - “You shall have no other gods before Me. You shall not make for yourself a carved image.”; implying the existance of “False Gods”. Similarly, in a later evolute we have - “Mohammed is the last prophet, and he supersedes all predecessors”. Hence, such religions are said to be defined in opposition to others.
विस्तारः (द्रष्टुं नोद्यम्)
Kenite Yhwist aniconic monolatry was not necessarily a counter religion, even if it had these 2 commandments - since it admitted validity of other ways for others.
Later Judaism, it’s mutant, which strongly based itself on invalidating surrounding natural religions (eg. proseletysim, iconoclasm, religious wars, Noachide Commandments, Rambam on cow slaughter), was one.
Modern Judaism appears to have reverted to the ancestral state?
Other religions might oppose each other - but not as a core definitional aspect. Further, they (objectively) claim to be a continuation or refinement of a prior natural religion. For example, a dvaitin vaiShNava can and does define his religious view without any reference to advaita; though he may reject the latter as a delusion.
Opposition in practice
Because opposition to/ rejection of prior natural religions is a core definitional (and not incidental) matter, such opposition becomes a core (and not incidental) part of practice. This often manifests both in ideal/ mythic practitioners as well as common laity. So, the muezzin shouts to the ummah- “There is no God but Allah” 5 times a day.
Indeed, for their inception and spread, they would have relied on such opposition to the extent of elimination. For the contemporary person, the absence of continued opposition leads to identity crisis: “Why did we separate from them? Why did our forefathers convert?” (akin to what a pAkistAni, whose nation was founded in opposition to united India, might confornt in considering the “two-nation-theory”).
Borrow and curse
Counter religions like Abe’s diseases, buddhuism etc.. emerge and copy-paste heavily from their prior natural religions (called the “borrow and curse” dynamic).
That does not make them the same or equally benign etc.. - Just as a cancer cell is mostly a copy of a healthy cell; but is sufficiently different as to proliferate and kill out all healthy cells; ultimately rendering the host crippled or dead.