I can understand why we don't have eclipses every month when the inclinations of the ecliptic plane and the moon's orbital plane are different. But the inclination of the moon's orbital plane changes from 18.5 degrees to 28.5 degrees and back to 18.5 degrees every 18.6 years (as a result of lunar precession). In other words, once every 9.3 years, the inclination should be 23.5 degrees, aligning the moon's orbital plane with the ecliptic plane. And yet, we don't see eclipses happening at every new moon and full moon when the two planes are supposedly aligned. Why is that?
There are few things here I think might be worth to state:
- The tilt of Earth is of no importance here. As the comment says what is of importance how much the Moon orbit is inclined to the ecliptic. Now, one can say that if both Sun-orbit and Moon-orbit have the same inclination to Earth equator (namely 23.5 deg) it means the Moon and Sun orbits have no inclination with respect to each-other - and they are actually on the same plane; But this is wrong conclusion. For not only the inclination itself is important but its direction vector also: i.e., where we reach the top/button. and where are the nodes (the points of intersection between the planes; on the Sun-orbit those also called equinoxes). So even if Moon's orbit were always inclined 23.5 to Earth equator, still it would not mean we would have eclipse every month -- we would only if the nodes are in the same position as the nodes of the Sun-orbit;
And this is exactly the catch here - when the Moon-orbit is inclined 23.5 deg to Earth tilt - this always happens in the same two specific directions of the inclination vector (against the equator). Those directions are not as the direction of the ecliptic inclination vector against the equator.
This is because the Moon-orbit is always tilt 5 deg. against the Sun-orbit (aka ecliptic). So in the period of this node precession of 18.6 years: when the limits collide (so also the node - so the direction vector is the same) the inclination to Earth equator is 28.5 deg or 18.5 deg; When they don't - the direction vector is not the same.
There is somewhat subtle issue here that cause me to edit this answer is that the node precession of Moon-orbit with respect to the equator is not complete. in the sense the nodes (again with respect to the equator) are not running over 360 deg in 18 years. But they run over much smaller span of maybe around 25 deg, ~12.5 deg from each side of the solar equinox. The precession works as regular (360 deg in 18 years) when we consider the nodes of the intersection not with Earth equator but with the ecliptic.
The precession of the moon's orbital plane does not align it with the ecliptic plane. The angle between those two planes is approximately 5.14° (it varies by ~±0.15°, mostly due to perturbation by the Sun). Precession causes the orientation of the lunar plane to vary, but the angle between the two planes stays (almost) the same. It's very similar to the precession of this gyroscope (courtesy of Wikipedia), except that the fixed point of the lunar plane is at the centre of the plane (i.e., the Earth-Moon barycentre).
As the gyroscope precesses, the plane of the gold disk maintains a constant angle to the horizontal plane.
So although it's certainly true that the angle between the lunar plane & Earth's equatorial plane varies between ~18° and ~28°, the angle between the lunar & ecliptic planes stays (relatively) constant.
It's difficult to draw a good diagram (or animation) to illustrate this. I've created an interactive 3D animation which may be helpful. ;) By default, it exaggerates the tilt of the lunar plane to 10° because it's a bit hard to see what's going on if you use the correct value of 5.14°.
As mentioned above, the lunar plane actually passes through the Earth-Moon barycentre (as does the ecliptic plane), but in this diagram those two planes pass through the centre of the Earth to keep things simple. That is, all three planes (ecliptic, equatorial, & lunar) pass through the centre of the Earth. The ecliptic plane is grey, the equatorial plane is blue, and the lunar plane is orange. There are matching coloured lines associated to the lunar & equatorial planes which show their axes and where they cross the ecliptic.
The large black circle in the centre of the diagram is in the ecliptic plane. The axis of the lunar plane touches the two small black circles at the top & bottom of the diagram.
You can rotate, pan & zoom on the diagram using the mouse, left mouse button, and scroll wheel. On a touchscreen, use 1 finger to rotate, 2 fingers to pan and zoom.
I recommend first toggling the equatorial plane off so you can more clearly see the basic precession of the lunar plane.
steps parameter controls the number of animation frames. Increase it for a slower, smoother animation.
The equatorial plane also precesses, but with a period of approximately 26,000 years. The lunar plane precesses with a period of ~18.6 years. Wikipedia has a good article on the various lunar precessions.
Here's a plot (courtesy of JPL Horizons) showing the small variations in the inclination of the Moon's orbit over a couple of years.