Is it okay to skip gears with a manual transmission? Ultimately, manual transmissions are designed with flexibility in mind. Inherently they allow for choosing any gear at any time, but that doesn't necessarily mean you should.
Of course, and gear you select, you need to make sure that the engine RPM will not exceed redline, and it's also wise to rev-match (or double clutch, if needed), as to not damage your synchronizers or clutch.
An unmatched upshift will result in a rough shift. An unmatched downshift can easily result in additional synchronizer wear, as well as clutch wear, and can also upset the balance of the car. That said, skipping gears, when matching engine RPM appropriately, does not cause any harm to the drivetrain, and is completely fine to do.