There is nothing wrong with the word "fruits". However, "fruit" is used in various ways, and some of them have some overlap with the ways "fruits" is used.
What’s “acceptable” seems like a matter of opinion. I just go with what sounds natural to me.
“fruits” as uncountable noun with plural verb agreement
The plural form “fruits” certainly exists. In its most traditional uses, it is not exactly “countable”, as it is used collectively or generally to refer to the products of something (either soil, or something more abstract). E.g., the Oxford English Dictionary gives the following quotations as examples for its first definition of “fruit”:
1725 I. Watts Logick i. vi. §3 If the husk or seeds are eaten, they are called the fruits of the ground.
1859 J. M. Jephson & L. Reeve Narr. Walking Tour Brittany ii. 20 The Breton peasant can turn all the fruits of the earth to account.
“fruit” as uncountable noun with singular verb agreement
The uncountable noun “fruit” (which takes singular verb agreement, like a mass noun) also exists. This is probably the most common use of the word “fruit”, so I won’t supply any examples.
“fruit” as countified mass noun, with countable plural “fruits” or “fruit”
Like nearly all mass nouns, this can be converted into a count noun “fruit” meaning “a type of fruit”, and this has a corresponding plural form meaning “types of fruit”. This plural form is often “fruits”, but I have found evidence that some people use “fruit” as a plural count noun. E.g.
Many fruit from the genus Vaccinium are rich in phytonutrients, including those with potent antioxidant properties.
– “Blueberry and Cranberry”, by Charles F. Forney and Wilhelmina Kalt, in Health-promoting Properties of Fruits and Vegetables, edited by Leon Alexander Terry
“fruit” as conventional count noun, with countable plural “fruits” or “fruit”
I agree with Peter Shor that when dealing with countable objects like apples, oranges and peaches, the most natural expression seems to be “pieces of fruit” (singular: “piece of fruit”).
However, some people do refer to these objects using the word “fruit” as a countable noun, with a countable plural form. As with the separate “type of fruit” use of countable “fruit”, it seems the plural form can be “fruits” or “fruit”.
Example of singular countable "fruit" in the sense of "a piece of fruit":
However, there is a particular point at which a fruit reaches what is described as the 'mature green' stage. While the fruit is developing, the surface has a slightly wrinkled, matt appearance. At this stage it is still immature
– A Post Harvest Handling System for Sweet Peppers, Research Division: Ministry of Food Production and Marine Exploitation
From one of these pips sprang the original apple, the present tree being a sucker which grew from the parent root. Though still green, it was very old and thin, and in 1901 had not borne a single fruit.
– Rural England, by H. Rider Haggard
Examples of plural countable “fruits” in the sense of “pieces of fruit”:
Examples of plural countable “fruit” in the sense of “pieces of fruit”:
The deep purple fruit has a waxy bloom, is round, and ranges in size from 0.6 to 1.2 cm in diameter and is borne in clusters of a few to many fruit.
– “Berberidaceae”, by Chad E. Finn, in The Encyclopedia of Fruit and Nuts, edited by Jules Janick and Robert E. Paull
There should be a preparatory thinning at the time of stoning, and a final thinning afterwards, because most plants, especially such as have overborne themselves, drop many fruit at that crisis.
– Abercrombie, in The New American Gardener, by Thomas G. Fesseden (p. 241)
For nondestructive evaluations, the same three fruit at each temperature were evaluated every second day; three additional fruit per storage temperature were removed every second day for destructive analyses.
– Something in the Proceedings of the ... Annual Meeting of the Florida State Horticultural Society, Volume 118 (sorry, Google Books only shows a snippet view and doesn’t show the full title)
By giving examples, I merely hope to show that all of the usages discussed here actually exist. I don’t know enough to describe their relative frequencies, or how they are distributed among different sorts of people. For example, it may turn out that one is agricultural jargon, or only common among ESL speakers, or a marginal usage that just pops up from time to time. Some of these could even be just typos or other kinds of basic production errors. I would love to see a more extensive analysis of the use of this word that revealed any of these things.
(Also, it's likely that one or more of the usages listed here sounds wrong to somebody. None of them are particularly grating to my ears, but I'm just one person.)
In this answer, I haven’t even gotten into the more marginal derived uses of the word “fruit” like the “fruit(s) of the Holy Spirit” in Christianity or the slang, commonly derogatory use to refer to a gay man.