Others have addressed the effects of air pressure and invasive species, but...
Depending on how you design your portal, you might have a problem with the portal itself
As the two planets orbit their sun, the portal will elongate, contract, rotate, and pass through the sun. As the planets rotate, the portal will pass through each and both of the two planets. Let's have some fun with this.
It becomes a pump As it lengthens and shortens the volume available for mass inside the portal increases and decreases. That's a pump. Which direction the pump will push air will depend on the air pressure on each side of the portal. Note that environmentally, that's going to change as climatic zones of high and low pressure come and go. That means the "wind tunnel" will in turn push in either direction. What's breathtaking is their delta-V. Earth books along at 67,000 mph. Mars (for example), books along at 54,000 mph. Max delta-V: 13,000 mph. that's a wind force that would strip plant life down to bedrock for hundreds if not thousands of miles in front of the portal entrances.
And then there's the heat The kinetic energy involved with the "motion" of the portal through space (call it the "wiggle" at the portal entrances) is well beyond non-trivial. I'm not going to try to calculate it, but it would easily vaporize water and probably vaporize rock.
Finally, there's two planets and a sun to contend with How gravity and the fusion forces of the sun affect passengers travelling through the portal during those periods when it must pass through the celestial bodies is, well, it's unknown, but it would cause a pretty bumpy ride. Worse, it could either super-heat the air as it resides inside the passage (which means it could be a 13,000mph plasma when it exits the portal) or simply create high/low pressure zones during the passage. Combined with the gravity "bumps" it could be like riding a rollercoaster that moves both above and below ground (hot/cold) and up and down (high/low gravity).
And that's all in a fraction of a second
Creating portals between two points in space-time that have no "apparent" distance is, basically, magic. Or, perhaps more scientifically, we don't really know what "distance" means when you warp space-time. We think we do, but it's all theoretical. As the author, you'll need to decide what happens between "in" and "out."
These give you some ideas of the complications of non-magical portal travel. Your story certainly needn't be as extreme as I've described (not by a long shot), but it can be made more interesting due to these "effects." For example:
a) There may be certain times of the year where portal travel is unavailable (e.g., due to passage through the sun).
b) The huffing and puffing of the wind as it's pumped through the tunnel could be used during a daring flight from danger as your characters must brave near-hurricane-force winds from the tunnel during their dash to safety.
c) The temperature changes can create unique environments near the portal entrances. In other words, during the middle of winter the portal entrance may be a lush, summery condition.