The whole vampire myths could be quite strange, since they of course come from Transilvania, Romania, but they may differ from country to country.
For instance my country Bulgaria borders Romania on our northern border and due some wars in the XX century some territories have exchanged ownership quite a few times, so there might be some cultural blending going on around the border territories.
However, I live in the southern parts of Bulgaria. And here in the small villages where part of my family comes from, pre-WWII there was a term called "going vamp" or "vampiring", something like that.
So in our mythology/lore it is believed that if a person dies and the body happens to be alone in a room where there are cats, if one of the cats happens to jump over the body - the person's spirit turns into a vengeful apparition that starts to harrass the family members or sometimes even kill them. My grandmother was actually telling us tales when we were young of a case in her village when it was believed that such a spirit had killed a little baby. I am inclined to believe her - pretty much every family member of mine has had some hard to explain experiences in that regard and while we are modern 21st century people, we have respect for the fact that those things while rare( the supernatural things) probably do exist and sometimes interact with people in different ways.
So there you go - a different take on the whole vampire thing, from a culture that's quite near to the origins of the myths.
As for the whole idea about vampires and werewolves not liking each other... I think it's a natural path for the creators and recyclers of myths to go. After all vampires and werewolves are the two most common myths of people living among people, but with a dark second identity hidden behind a mask of normality. So it's a very short way between thinking of the two most common wolfs in sheep clothes creatures and then pitting them against each other.
The world of full of myths and people who exploit them, sometimes with somewhat lazy worldbulding and such, so there's that.
The idea that vampires and werewolves hate each other is one popularized in recent fiction, but I've never encountered it in folklore. Possibly because they almost never appear in the same folktales together. Or maybe that's why they so rarely appear in folktales together, because no antipathy means probably no conflict and no conflict means having them both in a single story makes one or the other of them superfluous. (How many monsters does one folktale actually require, after all?)
Although I do know that there were some places where people used to believe that werewolves became vampires after death.
I doubt there's any basis for this in folklore: I'm pretty sure werewolves and vampires come from different folklore traditions in Europe (the name is a dead giveaway here: "were" or "wer" is an old word for "man" in the Germanic languages, not the regular one any more in any language as far as I can tell, but vampire appears to be a Slavic word).
I think in fiction, before urban fantasy came along, you wouldn't normally have both vampires and werewolves together in one story: you'd have a vampire story or else a werewolf story, and that would be that. Somewhere in there urban fantasy starting throwing all these notions together, and I guess it just makes for more interesting fiction if they don't get along--an easy default, more story-generating potential. So, as I think someone else suggested, probably an invention of 90s fiction (and TV--surely there were werewolves in Buffy? I wasn't ever much of a fan, so I don't remember).
But there are men who turn into wolves in other traditions. For instance, the French Loup Garou. These stories spread across Europe. We are most familiar with werewolves under that name, but that doesn't mean the idea originated in Germanic countries. I doubt there is any way of telling where they originated. But there are legends all over the world of what we would call were-beasts of one sort or another.
These stories are very old. Modern adaptations tend to embellish them quite a bit until many readers begin to believe that the embellishments are part of -- inseparable from -- the earlier legends, when they are no such thing.