Stop saying that it's not possible to be vampire and werewolf. I use clean Legendary edition and i had some completely functional Werewolf/VL hybrids.
I'm playing Skyrim Legendary edition on PC (no mod added). I became hybrid after i finished Dawnguard DLC (i killed Lord Harkon). I only found one glitch so far:
First time i became hybrid, i farmed for a while in werewolf form until i got all the perks. Than i tried to lvl up my VL perks, but i notice i don't get any perk experience by killing with Drain life spell of Power attack bite.
I had to load just before i became hybrid to get all VL perks (you can get location for all the forts by activating those red and blue flags on a map that you can find in any keep). Visit all forts and exterminate those weak bandits. You can also gain perks by killing (with Drain life) any hostile animal you encounter. Add some random encouters with thalmor or imperials leading some prisoners and your perk will advance fast.
Once i got all 11 perks for VL, i become hybrid and i farmed (again) to get all werewolf perks - Savage feeding helps a lot here. Even rabbits, foxes, deers or other animals can be consumed to gain perk experience, so make sure you unlock that perk as fast as you can.
Since i never feed (as a human vampire), i'm at "stage 0" vampirism in human form after i revert from VL (you are undead, so you are affected by Necromage perk, you can use Vampire Sight but you are not affected by sunlight and no weakness to fire), but when i use VL power, i gain all powers and weaknesses from stage 4 vampirism. I also tried to use all nightpowers and blood magic and i haven't found any problems (in VL form). You cand use life drain spell and bite power attack, but you don't get perk experience, so don't forget to lvl up yout VL perks before you turn into a hybrid.
After you revert from Werewolf form, you are a normal human (you are not affected by Necromage perk, you can't use Vampire Sight...), so make sure you use VL power and revert after a hunting season as Werewolf (for boosted echantments and othe bonuses you may get)
I have necromage perk, so all my armor echantments are 25% stronger (i always use VL form then revert after a hunting season as werewolf to make sure any bonus i get is boosted by Necromage), i have 100% spell absorption with Atronach stone and Atronach perk, and many other boosted effects.
All werewolf perks are working.
So here's a recap:
1. Complete Dawnguard DLC (sides doesn't matter).
2. Advance in Companions quest line until they tell you to meed at the Underforge.
3. Get all the VL perks.
4. Have Serana to follow you.
5. Equip VL power.
6. Go to the Underforge and make a save.
7. Press to drink the blood and VL power button at the same time.
You should appear in Whiterun as a werewolf for an instant, then turn into VL.
8. Use revert form as soon as you can.
If you reverted to Human, it's a success and you can continue with the next step. If you revert to werewolf form, you have to reload and try again.
9. Ask Serana to turn you into VL again.
10. Turn into werewolf to continue with Companions questline and farm for werewolf perks.
11. Remember to use VL form and revert after a hunting season as Werewolf.
I also read about becoming a hybrid before Dawnguard DLC was out, but that version was really bugged.
This is how it worked:
1. Complete the Companion quest line untill they tell you to go to Underforge.
2. Find some vampires and let them use Drain life spell on you. Whe you see the massage "you have contracted Sanguinare Vampiris", take a note of in-game time and date.
3. Go to underforge and wait exactly 72 hours since you contracted the disease. You have to drink the blood when you recive the message that you have progressed to stage 4 vampirism.
I haven't tryed this metod, but others did it and they said it can cause some problems like not being able to feed, so you are always at stage 4 vampirism, making others to become hostile.