No, the liver can process at least 25 grams of fructose per day. Most fructose is coming from sucrose as sucrose is half glucose and half fructose. 25 grams of fructose a day baseline is probably beneficial because the liver is made to handle about 25 grams of fructose a day (though alcohol consumption interacts similarly so high alcohol intake will reduce fructose that is “good”). Fructose and Alcohol in moderation actually may stabilize blood sugar. Fructose, because it does not need insulin to be used, and alcohol because it occupies certain enzymes which would otherwise cause glycogenolysis (release of glucose from the liver), but above 25 grams of fructose+alcohol and the liver tends to not keep up with turning fructose into liver glycogen, and so it makes fatty liver and insulin resistance. If you exercise hard, the liver has more space to put the fructose and so you can probably add more if you exercise hard. Most estimates are that at about 500 calories an hour 250 will come from carbs, and 1/3 of that can be restored by fructose without a problem, so an hour of hard work can allow for quite a bit more (about 80) grams of fructose and at higher workloads it goes up even more. Alcohol too.
Regarding fruit then, even a high sugar fruit like cherries, grapes, oranges only has about 8-9 grams of fructose for a 5 ounce serving. Strawberries only have about 10 grams of sugar (5 grams of fructose) per 5 ounce serving. Watermelon and Cantaloupe have about 5 per 5 ounces, and bananas only about 10 for five ounces which would mean that you could eat 3 x 4 ounce bananas a day without hitting 25 grams of fructose, and more if you train hard. A 32 ounce soda can have up to 60 grams of fructose.