You can travel with pretty much zero carbon footprint (look into bicycle touring or long distance hiking). So a large carbon footprint is not inherent to travel.

On the other hand, you can hop around with planes all the time, even for short distances. That has a huge carbon footprint.

And then there are things in-between, e.g., occasional plane flights and lots and lots of public transportation (trains, ferries, and buses). That's where I am at mostly.

So it's a spectrum and I'd encourage everyone to at least think a bit about their environmental impact.

But overall, I think traveling long-term allows you to reduce your carbon footprint a lot if you want to see the world. If you only have 2 weeks, there's often no way around taking a bunch of flights. If you have 3-6 months or more, you don't mind taking 10-30 hour rides on public transport.