“Huh, I assumed because the Ivy League plays D1 b-ball and soccer that they were in the FBS. Learned something new today.”
There’s multiple layers within D1, all driven by football.
Lowest is FCS, where the Ivy and Patriot Leagues are.
Middle is lower tier FBS, which is where you find Rice (Conference USA) or Tulane (American Conference).
Top is FBS Power 5 Conferences (Stanford, NW, Vandy, Duke, ND). Which used to be called BCS football. Full monty football, and tend to be full monty for other sports too.
In D1 hoops, for example, everyone technically plays the same level and can make the NCAA tourney. But as a practical matter, you really only see Power 5 teams competing at the highest level. With a few exceptions (Gonzaga or Big East teams like Gtown and Villanova).
In the niche sports that don’t make money and game attendance often measures in the dozens or hundreds (baseball, lacrosse, soccer, etc.) the playing field is more level. So while the Power 5 schools still dominate, you do see more outliers – like the Ivies in lax and ice hockey.