I was told once, long ago, that cases in which small animals fail to accept each other can sometimes be helped by giving both animals a bath (separately and privately, of course) so that their respective odors are changed slightly. With visual and other cues already established, the change - or temporary reduction - in "personal smells" permits the two to re-extablish their "opinions" of each other.
I must say that I've never had occasion to try this out. The critters that elicited the advice belonged to someone else, who never reported whether it was tried; and we haven't had a need with any of our little ones.
Most dogs I've known tolerate bathing fairly well, but the response from cats is variable. We have had cats that we bathed regularly while living in a place where fleas were frequently "imported" from external sources over which we had no control, and they learned to enjoy it; but a first-time experience can be stressful for some cats - and hazardous to the "attendants."
The advice wasn't specific as to whether the same soap should be used on both, to make them smell alike, or whether the intent was just to "change each of them" to something different. Since most "pet shampoos" include other treatments, and dog and cat "flea soaps" especially should not be used cross-species, perhaps a simple baby shampoo or similar would be best for both if you consider an experiment with the idea.
A more commonly recommended procedure is to give each animal its own space for a while. After each has had time to "establish a presence," in this case you would let the cat into the dog's space after temporarily removing the dog, to let the cat sense "dog has been here" for a few hours, before making a new attempt to introduce the animals to each other. I have heard claims that this has been successful, but with many living arrangements the difficulties of arranging the separations don't permit effective use of the method, so failures are also fairly common.