I know it's probably been asked a few times and I've read different views on this, but when a ship is moving through or near a asteroid does it's base making contact along the path count as hitting the obstacle? I've gotten different opinions from people. This is something that really needs to be put in the official FAQ.

The base of a ship doesn't move along the path of the maneuver template

p4 of the rules reference:
When a ship executes a maneuver, it is picked up from its starting position and placed in its final position. The full width of the ship’s base is ignored except in its starting and final positions

so No, only if the maneuver template or the base in its final position makes contact it counts as a hit

The only time anything like this would happen would be if the final position of the ship would overlap another ship. In that case the ship would be moved backwards along the template until it is no longer overlapping the other ship's base. This may result in the final position of the ship overlapping an obstacle.

This might be where the confusion arises.

However it is still the final position of the ship's base that determines whether it has overlapped the obstacle

Just as an addition to this, If you end up overlapping on one, next turn you don't take the penalty if you clear it?

As I've seen some people play it as if you overlap and next turn when you pit your movement marker down if that doesn't touch the obstacle ita fine, but if it does even if you clear it you take the penalty again?

Just as an addition to this, If you end up overlapping on one, next turn you don't take the penalty if you clear it?

As I've seen some people play it as if you overlap and next turn when you pit your movement marker down if that doesn't touch the obstacle ita fine, but if it does even if you clear it you take the penalty again?

If the template or the ships final position overlaps an obstacle, you suffer the concequenses of it. Where you started from is irrelevant. So you have seen people play it correct

Just as an addition to this, If you end up overlapping on one, next turn you don't take the penalty if you clear it?

As I've seen some people play it as if you overlap and next turn when you pit your movement marker down if that doesn't touch the obstacle ita fine, but if it does even if you clear it you take the penalty again?

If you overlap an obstacle, you take the penalty. In the next turn, if your ship or maneuver template overlaps the same obstacle (or another one), you take the penalty. If your ship was just resting it's nose or nubs on the obstacle, then chances are the following turn your template is going to overlap it too. This is where having an ability to barrel roll off to one side can save you, as long as the template doesn't overlap any part of the obstacle.