They are not realistic but when it comes to defects of the film process there's one they replicate very well: reticulation. When you sharpen a Fuji file it displays a type of artifact that people have come to call "Fuji worms". It's similar to botching the bleaching stage when developing film.
Now, if you're after the colors of film, look elsewhere. Fuji has an inferior color filter array, particularly in newer generations where autofocus creates an ugly problem where you have entire rows of pictures with no green data. The colors in the older models are slightly better than the new ones but AF is slow.
If you want the ultimate filmlike experience take a look at Sigma and their Foveon sensors. The most color accurate cameras in the market. After that, Canon, Nikon and Pentax have your back. Olympus and Panasonic produce beautiful results but their sensor is tiny so it can be limiting. After that, Sony. Technically not bad but they demand a lot of postprocessing to look good. Capable of beauty but dull by default. Fuji is last place, unless you want to shoot people pictures and then it's nice. It's ironic because they produce arguably the most beautiful film stock in the market, Velvia. However, even their Velvia simulation doesn't come even close to the real thing, while Sigma can achieve that and more. One of the easiest ways to get close to the film look is shooting RAW and then using presets in Lightroom. Look up RNI labs. You can get the packs pirated if you want. The Fuji sims are similar to this but in camera and with inferior results because of the sensor. Even adjusting the parameters of the simulations with "recipes" it's not even close to the real thing.