No, the Earth's axis isn't tilting wildly due to the ice caps melting.

I have received several emails about a website claiming that the Earth is tilting wildly from its usual 23.5° inclination, and that this is causing

How We Know Today's Climate Change Is Not Natural

Breaking News English, 2-Page Mini-Lesson

Shouldn't the tilt on the Earth's axis be considerably insignificant compared to the overall distance from the Earth to the Sun? Why is there such a large temperature change from season to

Melting Glaciers Have Shifted the Earth's Axis - GlacierHub

Environment News - TheUNN

If the change in season is due to the tilt of the earth, how come the polar ice isn't melting every season? - Quora

Glacial melting from climate change shifted Earth's poles

Melting Polar Ice Caps Distributed Enough Water to Cause a Shift in Earth's Crust Horizontally, Study Reveals

Melting Glaciers Have Shifted the Earth's Axis - GlacierHub

global warming Musings on Maps

Solar system planets, order and formation: A guide

Does Melting Polar Ice Affect Earth's Tilt and Spin? - The New York Times

Melting ice sheets changing the way the Earth wobbles on its axis, says Nasa, Climate crisis