According to The Strange And Incredible Saga Of Willow and Tara On "Buffy the Vampire Slayer", there was initially at least some backlash from some fans about the relationship.
The storyline received a great deal of attention in the press and sparked a controversy that divided the show’s most loyal fan base. In fact, Amber Benson who played Tara experienced first hand just how nasty the fans could get. She would visit the Buffy posting boards on the web on a regular basis and discover that negative comments were not only being made about the Willow/Tara relationship in general, but that the fans were targeting both the character of Tara as well as Amber Benson herself. “It was just so surreal to have people using my name and Tara’s name interchangeably and saying nasty things about both,” she said in the October 2000 issue of the English Science Fiction/horror magazine Dreamwatch. Benson also went on to say in the interview that ” it hurt for people to make nasty comments about Willow and Tara’s relationship and about my weight and what I looked like as a whole. Whether someone says that your ugly to your face or on a posting board, it still hurts horribly. I mean, you wouldn’t just go over to Joe Blow and say, ‘I think you’re a fat, ugly sexual pervert.” Almost immediately websites showing their support for Benson began popping up all over the web . “I have gotten so many supportive letters from fans,” Benson said. They have been so kind, she said. “they make me feel better about everything , especially when they share their experiences. They make me realize that I am not alone. We are all beautiful no matter what we look like on the outside.”
The article also goes on to explain why there was no on-screen kiss between Willow and Tara until season 6.
Hannigan also went on to talk in the interview about how the WB network would not allow an onscreen kiss between the two actresses ” In America we’ve not been allowed to have the kiss on screen. As actors, we sometimes get the squished down version of reactions, so it could be that The Powers That Be are freaking, but to us it doesn’t seem like a big deal. The show goes out at 8:00 p.m., the first hour of prime time. If it went out at 9:00 p.m., we could probably show a kiss, but why bother ? I don’t think we need to see it. It’s just the annoying fact that we see Buffy and Riley having full--- on sex all day and all night (in Where The Wild Things Are.), but these two girls can’t even kiss ?”
The show moved from the WB to UPN after season 5, so apparently that network was a little bit more progressive-minded about the relationship.