Nathan Tobey went to a Phish concert hoping to enjoy the medley of song improvisations and laid-back vibes that have drawn followers to the band for more than three decades. Instead, he found himself in the middle of a vicious battle for real estate.

When the gates at Virginia’s Hampton Coliseum finally opened after an hourslong wait, Mr. Tobey rushed to stake out a choice seat on the first row of the balcony. Seconds before he got there, another fan swooped in and covered the entire row with a giant tarp, grabbing all eight seats.

“I’m a very mellow guy, but we had some words,” said Mr. Tobey, a 37-year-old podcast producer from Minneapolis who has been to 70-odd shows. “I had to assert—as a fellow fan—that this is not fair.”

Fans fight about “tarping” pretty much anywhere there is a band on stage and general-admission seating up for grabs. But easygoing Phish fans—or Phans, as the tie-dyed die-hards are known—fighting? That’s a bummer, man.

Phish, currently on a normally cheery summer tour, has sold more than eight million albums and DVDs in the U.S. since emerging from the Vermont college-rock scene in the 1980s, drawing a flock with a chilled-out, neo-hippie ethos. As the band’s security procedures manual once said, its fans are a “peaceful, intelligent group” who will “dance and twirl in any open area made available to them.”