We studied the effects of cluster environments on galactic structures by using the TNG50 cosmological simulation and observed galaxies in the Fornax cluster. We focused on galaxies with stellar masses of 108 − 12 M⊙ at z = 0 that reside in Fornax-like clusters with total masses of M200c = 1013.4 − 14.3 M⊙. We characterized the stellar structures by decomposing each galaxy into a dynamically cold disk and a hot non-disk component, and studied the evolution of both the stellar and gaseous constituents. In TNG50, we find that the cold (i.e., star-forming) gas is quickly removed when a galaxy falls into a Fornax-mass cluster. About 42%, 73%, and 87% of the galaxies have lost 80% of their star-forming gas at 1, 2, and 4 billion years after infall, respectively, with the remaining gas concentrating in the inner regions of the galaxy. The radius of the star-forming gaseous disk decreases to half its original size at 1, 2, and 4 billion years after infall for 7%, 27%, and 66% of the galaxies, respectively. As a result, star formation (SF) in the extended dynamically cold disk sharply decreases, even though a low level of SF persists at the center for a few additional gigayears. This leads to a tight correlation between the average stellar age in the dynamically cold disk and the infall time of galaxies. Furthermore, the luminosity fraction of the dynamically cold disk in ancient infallers (i.e., with an infall time ≳8 Gyr ago) is only about one-third of that in recent infallers (infall time ≲4 Gyr ago), controlling for galaxy stellar mass. This quantitatively agrees with what is observed in early-type galaxies in the Fornax cluster. Gas removal stops the possible growth of the disk, with gas removed earlier in galaxies that fell in earlier, and hence the cold-disk fraction is correlated with the infall time. The stellar disk can be significantly disrupted by tidal forces after infall, through a long-term process that enhances the difference among cluster galaxies with different infall times.