Your logic is flawed. The Milky Way doesn't follow lie along the equator because the earth is tilted on it's axis.
The fact that we can see other pulsars (many of them) from within the Milky Way means that those pulsars are either rotating on an axis nearly perpendicular to the galactic plane (aka galactic equator), or they're tilted relative to to the galactic plane and we happen to be nearly perpendicular to their axis of rotation. Since we know that not all stars rotate in the galactic plane (e.g. the solar systems ecliptic plane is inclined about 60 degrees from the galactic plane, and we have now observed enough other planetary systems to know that isn't uncommon), then it's likely that some of the pulsars we can see are spinning approximately in the galactic plane, and that some are not. But given there are many more random orientations that are not on an axis perpendicular to the galactic plane, it's probable that most of the ones we can observe from earth are nearly perpendicular to the galactic plane, and will thus be visible throughout most of the galaxy. As we travel around the galaxy within the vicinity of the galactic plane, the pulsars we can see from any given point will be those that spin on an axis nearly perpendicular to the galactic plane, plus some smaller number at other orientations that happen to have an axis of rotation approximately perpendicular to a line between that point and the pulsar.
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