Many people say that stars twinkle because of Earth's atmosphere. However, the atmosphere is still there when we look at planets and don't see they twinkling.
Is there a clear scientific consensual explanation for the twinkling of some objects but not for others?
Note: just as a metter of distinction, my question is different from this one. In fact, the moon is obviously different from stars, while my question is based on the fact that the only actual difference between stars and planets is that planets move across the sky, differently from stars (since they are the sky's reference). Proof of my words is the late distinction of Uranus as a planet due its extremely slow motion, although it also doesn't twinkle.
The answer to this is that stars are effectively point sources, but planets have disks. Borrowing the link to Sky and Telescope's explanation from @N. Steinle's comment.
The way I envision it is to think of the light from a celestial object as a fiber optic cable, continually being snipped at with scissors (which stand in for atmospheric turbulence changing the path of light traveling through it). The cable from a star is a single glass fiber with a very bright beam shining down it. The cable from a planet is a thick bundle of fibers with a much dimmer beam shining down each fiber in the bundle (compare the surface brightness of Mars with the surface brightness of the Sun)-- the total amount of light coming through the cables is comparable. The scissors can cut through the single-fiber cable completely, but they can only take out a few strands of the thick bundle. So atmospheric turbulence can cause the light from a star to be drastically interrupted, while the change for a planet is much less. Therefore, there is visible twinkling from stars, but not from planets.
Thought I'd add on the above. Starlight is like a very narrow laser beam pointed at you. A planet is like a bunch of those arranged in a circle all pointed at you. Any one of those lasers can be deflected by the atmosphere. There is only one to deflect in the case of star light. There's several in the case of a planet. If any few lasers deflect, there's still plenty that are undisturbed.
Light from both stars andcplanets deflect. The planet is less like a point source. Still deflects, but the spread of source points compensates.
Apparently both planets and stars can twinkle when closer to the horizon. There is more deflection. This works to offset the spread effects. Can't say I've witnessed this personally though.
Planets do definitely twinkle sometimes, and stars don't always twinkle as much. It's not a binary yes-or-no, it's a continuum.
Even Venus can be seen twinkling if it's close to the horizon and the atmospheric turbulence (a.k.a. "seeing") is bad.
As for why stars twinkle more easily than planets, you've received some answers already.