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

Scientists ID Three Causes of Earth's Spin Axis Drift

Earth Had a Dangerous Axis Tilt 84 Million Years Ago, Shows Research

Environment News - TheUNN

If all of Earth's ice melts and flows into the ocean, what would happen to the planet's rotation? – Climate Change: Vital Signs of the Planet

Melting Glaciers Are Wreaking Havoc on Earth's Crust, Science

Earth Axis Tilt Change Caused by Melting Ice

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

Melting Glaciers Have Shifted the Earth's Axis - GlacierHub

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