Yes, various Gods (capital ‘G’) exist.
Whether adherents of various religions chose to believe or accept each others’ deities does not change their existence.
Under the rules of grammar, capitalization applies when a proper noun refers to a specific individual. We do not capitalize words like humans, tigers, meadowlarks, etc. because these refer to a group and not a specific individual. If gods exist, there would be no need to capitalize the word because in this capacity the word gods does not refer to a specific individual.
On the other hand, when referring to the Uncaused Cause of all that exists (aka God), we are necessarily referencing one specific being who is Being Itself, whose essence is Existence Itself. Ipsum Esse Subsistens. In this case, and only in this case, is God, under the rules of grammar a proper noun that is capitalized because only this “God” is one individual that the word God references.
If pagans choose to honour gods, whether existing in reality or not, is neither here nor there, because ultimately these gods cannot account for reality itself. Since ultimate reality is one, the question remains, “Is there one supreme God that accounts for all of reality and is the one Supreme Deity over all?”
This, I submit, is the difference between paganism (which honours ostensibly “higher” beings) and monotheistic religions that propose one Supreme Being over and above all that exists and explains all that exists, including those domains inhabited by pagan deities.
So your comment “…whether adherents of various religions chose to believe or accept each others’ deities does not change their existence…” applies here as well, but even more so because if one Supreme Being exists then that God is due honour and worship far above all other gods. Whether adherents of pagan religions choose to believe that or not is irrelevant and as you say “does not change” his existence.