I don't think there is any way right now to come without negatively affecting the locals. Essentially, the tourists to locals ratio is out of hand. A few of the problems we are facing:

1. Everything is overcrowded. Our public infrastructure is barely equipped to handle the population of 10M, on top of that add the 36M visitors we saw in 2023. It may be fun and exciting if you are here for a couple of days, but living through that all year long is exhausting.
2. Everything is overpriced. Most people coming to Greece have expendable income we don't have, along with overcrowding, this sets prices we cannot afford. Airbnb has definitely exaggerated the housing crisis, but it's not the only issue. When you are eating, drinking, visiting historical sights, or doing any activity, you are contributing to that.
3. Our economy is over-reliant on tourism. As someone else commented, no other type of industry can compete with tourism, every year more places lose their identity as they adapt to the ever-growing needs of the tourism industry.
4. Our history is being erased. Visiting a historical sight may a wonderful experience for you, but every step you make, every photo you take, every trash you throw, impacts the place you are visiting, destroying little by little thousands of years of history.

As a personal note, my income is a few times the national average, and yet I cannot afford to go on vacations this year...

As a (not) fun challenge you can try to limit your budget to around 30 eur per day per person. You will fail, probably won't even find living accommodations within that budget, but it will give you an insight on our struggles.