TL;DR: I believe that Homalinotus histrix is the (correct) original spelling and should be retained

This is an interesting case. In the printed text containing the original description of Curculio histrix Olivier, 1790, the name is clearly spelled using the 'i' in both instances it is mentioned [1]. This was "corrected" by Fabricius (1792) [2], and appears (in the copy available on BHL, at least) handwritten (in the combination Rhynchaenus hystrix, used by Fabricius (1801) [8]) under the illustration of the weevil in the supposedly subsequently published (1808) plates which accompanies Olivier's work [3]. This spelling has subsequently been used by many authors (though mainly cataloguists, it appears), including the influential catalogue of South American weevils [4].

However, in the definitive revision of Homalinotus that remains the most recent and most comprehensive treatment of the genus [5], Vaurie uses the "histrix" spelling throughout. Unfortunately, she doesn't discuss the different spelling of the name.

The International Code of Zoological Nomenclature [6] considers that the original spelling of a name is to be preserved (Article 32.3), unless it is an incorrect original spelling (Article 32.5), deemed as:

If there is in the original publication itself, without recourse to any external source of information, clear evidence of an inadvertent error, such as a lapsus calami or a copyist's or printer's error, it must be corrected. Incorrect transliteration or latinization, or use of an inappropriate connecting vowel, are not to be considered inadvertent errors (Article 32.5.1)

Although I make no claims about being particularly proficient in Latin, a quick check of an online Latin dictionary [7] indicates that both "histrix" and "hystrix" are acceptable spellings for the Latin word for porcupine. As such, I don't see evidence here that Olivier's original spelling of "histrix" is an incorrect original spelling that needs to be corrected in the sense of the Code. This makes Fabricius' change in spelling an unjustified emendation (Article 33.2.3).

The Code does make a provision for continuing to use an unjustified emendation in the event of prevailing usage (Article 33.2.3.1). However, I believe that the usage of "histrix" by Vaurie (1973) and (following her lead) on iNaturalist makes it difficult to claim that the unjustified emendation "hystrix" should be retained.

REFERENCES
 
[1] Olivier, G. A. (1970). Histoire naturelle. Insectes. In Encyclopédie méthodique. Histoire naturelle des animaux. Paris, vol. 5, page 503.
https://www.biodiversitylibrary.org/page/7577629

[2] Fabricius JC (1792). Entomologia systematica emandata et aucta. Secundum classes, ordines, genera, species adjectis synonimis, locis, observationibus descriptionibus Part 1, page 425.
https://www.biodiversitylibrary.org/page/52755909

[3] Olivier GA (1808). Entomologie, ou, Histoire naturelle des insectes : avec leurs caractères génériques et spécifiques, leur description, leur synonymie, et leur enluminée Coléoptères Volume 8, Plates 66--100 (Specifically, No. 83, Charanson, Pl. XV, Fig. 182)
https://www.biodiversitylibrary.org/page/40640119

[4] Wibmer G, O'Brien CA. (1986) Annotated checklist of the weevils (Curculionidae sensu lato) of South America (Coleoptera: Curculionoidea). Memoirs of the American Entomological Institute 39, page 128.
Not available online :(

[5] Vaurie PA (1973). The weevil genera Homalinotus and Ozopherus of the Neotropical Cholinae (Coleoptera, Curculionidae). Bulletin of the American Museum of Natural History* 152, page 31 and elsewhere. http://hdl.handle.net/2246/600

[6] https://code.iczn.org/formation-and-treatment-of-names/article-32-original-spellings/?frame=1#art-32-5

[7] https://www.online-latin-dictionary.com/latin-english-dictionary.php?parola=histrix

[8] Fabricius JC (1801). Systema Eleutheratorum : secundum ordines, genera, species, : adiectis synonymis, locis, observationibus, descriptionibus Volume 2, page 462 https://www.biodiversitylibrary.org/page/63318145