- If the rings intersect, they'll clearly knock each other out of the sky. So for this to even be plausible, you'd need one ring at a distance and another ring close in.
- But rings are in orbit -- they're constantly orbiting the planet. And the rate of their orbit affects how far out they are.
- Particles tend to lose energy over time and fall inward. That means an outer ring interferes with an inner ring.
- The interference is not destructive if the two rings are going the same way. The interference is destructive if the two rings are going different ways.
- Worse, any ring not on the plane of the planet's equator will degrade overtime because of differences in gravity caused by the spinning planet. They'll flatten out.
Summary: long before a bunch of random particles has time to form a stable ring, they will be pulled down into the plane of the equator and be forced to generally be going the same direction.
You COULD have an artificial ring. Our various TV, spy, weather, etc. satellites orbit Earth at various distances. Those that are in non-standard orbits either decay or have a way of repositioning themselves. Put enough such items in orbit, Earth would have a ring.
So, if your intrepid explorers do find a planet with rings going in several directions, they should definitely be looking for sentient aliens.
Two useful sources: