The problem is that radio altimeters are pretty old, and their filtering technology is not great. So even though they are filtering the 3.7-3.98 GHz 5G band, it's not as effective as a modern RF system/filter would be. Previously, this wasn't the issue because nothing was broadcasting in that band at particularly high power.
That's the second component of the problem: power. The radio altimeter system is capable of handling some amount of noise power caused by unwanted broadcasts, among other things. Previously, satellites were using this band, and they were so far away that between the distance-based attenuation of the signal and the limited filtering, radio altimeters could operate unaffected.
5G is a different story, though. The towers are much closer to the runway, so the leakage power is much higher. Whether this actually causes a problem for the altimeters is then dependent on a number of factors, including the distance to the 5G tower, the transmit power level, the direction of the 5G antennas, etc.
Could it cause a problem? Sure. I bet if you pointed a directional 5G antenna straight at a particularly crappy radio altimeter, you could materially affect its operation. But there are many mitigation strategies that could be used, like requiring lower transmit power, further antenna distances, appropriate directional transmissions, etc. These strategies have been used successfully in other countries.
The real concern should be the total lack of collaboration between the FAA and FCC. It's turning into a jurisdictional pissing contest.