there is or there are is decided by the number of the things that is associated with "there". There is a dog, there are two dogs, is there a dog? Are there two dogs?
Is there an objection, are there any objections, is there any objection? any objection at all?. The verb number depends on the number of the associated thing. Whether you decide to say "is there any (something)" or "are there any (somethings)" depends on if you seek a single answer or an unknown number that could be more than one.
The choice of verb number (and singular/plural of the thing) defines which specific type of answer that you seek: a single exception or a number of different exceptions, perhaps as many as people can provide. If I only want one answer, any answer at all (not any answers at all meaning as much as all that could exist but also possibly only a single answer), then I would say "Is there any something".
The idea of any does imply a choice of multiples, but you can define the question in terms of a single option as the answer and still have an unrestricted range of possibilities for that single answer. Any answer is better than no answer, say. Clearly, "any" implies that there are innumerable answers. But I do not care about them all, I care about one. My needs become satisfied with any single answer of the many that might exist when I ask "Is there any...?"