There seem to be a fair number of possible exceptions, so the rule that you learned about the formation of future active participles (-ūrus participles) doesn't seem to be any kind of absolute rule, only a rule of thumb that is true for "regular" verbs. Hale and Buck's Latin Grammar (1903) mentions this phenomenon and gives some other examples of exceptions.
It seems the usual identity of the stems for the perfect and future participles may be coincidental. In "Participles and nominal aspect", Eva-Maria Remberger writes that
The form of the FPart [...] probably represents a derivation of a supine in the form of a locative, ending in -tū (Leumann et al. 1963: 342); however, later it was interpreted as being derived from the stem of the PPart (cf. Ernout 1953: §320, among others). Nevertheless, these latter assumptions are contradicted by a large number of exceptions which clearly are not derived from the stem of the PPart. The following FPart forms are all derived from the stem of the present and not the PPart: [...]
(Note: I have removed the list of forms mentioned, as they are included in my own list below)
Moreover, there are verbal paradigms which have a FPart form without displaying a PPart form, at least in Latin, like fugitūrus, futūrus (cf. Leumann et al. 1963:342).
(Inflection and Word Formation in Romance Languages, edited by Sascha Gaglia and Marc-Olivier Hinzelin, p. 273-274)
There seem to be a few possible complicating factors that have made it tricky for me to figure out the patterns for these kinds of exceptions, and which words exactly are exceptions.
Complication #1: it seems Latin supines often had variant forms
One complication is that many verb stems in Latin seem to have had alternative forms based on phenomena like syncope and contraction. In some cases, the stem used for future active participle seems to be a less common (it looks to me, usually less contracted) alternative form of the supine stem, so it's hard for me to tell how many of these represent a situation where one stem is exclusively used for the supine and another exclusively used for the future active participle. For example, it seems that paritus existed as an alternative form to partus. (On the other hand, I have found a few sources that indicate that "partūrus" was not really used: Zibaldone, by Giacomo Leopardi (2013) & Grammatical Commentaries, by Richard Johnson (1718).) Johnson has a section "Of the Formation of Supines, and Participles in us and urus" (p. 377) that mentions some more possible examples of non-matching forms.
Complication #2: Could "irregular" participles really be derived adjectives in some cases?
I'm also not sure if some cases might be situations like English "drink, drank, drunk" vs. "drunken" or "melt, melted, melted" vs. "molten" where one form might be used for the participle (inflected form of a verb) and another form is used for a derived adjective.
Some Wiktionary entries that I have read seem to give this impression; e.g. the Wiktionary entry for nascor says "Note: Future participle is sometimes nāscitūrus" while the primary Wiktionary entry for nasciturus defines it as an adjective that "has the form of a future participle of nāscor".
Similarly, Excerptiones de Prisciano: The Source for Ælfric's Latin-Old English Grammar, edited by David W. Porter (2002), contains a passage mentioning the use of "cariturus" alongside "cassus" (p. 272), but the Wiktionary entry for cassus calls it a "verbal adjective" rather than a "participle".
Modern linguistic analyses of languages like English often draw a clear distinction between participles (analyzed as inflected forms of verbs) and derived adjectives, but the tests for distinguishing these can be fairly complex and often only apply in very specific situations. I'm not familiar with what criteria, if any, can be used to distinguish deverbal adjectives from verb forms in Latin. (I asked this as a separate question, and it seems that the main criterion that would establish participle-hood in Latin is taking an accusative direct object, which is only relevant for transitive verbs.)
Despite these complications, there do seem to be other examples
But there definitely seem to be cases where, even if the alternative, less contracted stem is not exclusive to the future active participle, the alternative stem is more common in the future active participle than in the supine/perfect participle.
Examples categorized by ending
A. In -ātūrus, from first-conjugation verbs with past participles not ending in -ātus.
stātūrus from stō, stāre, stetī, stătus.
Mentioned in brianpck's answer to "Is cultura a future participle?" and TKR's answer to "Stem for derivatives like figura, statura and cultura". Neue and Wagener have a long list of sources that attest to the length of the a in this future active participle (p. 590).
Some online sources e.g. Wiktionary give the form "statūrus", but it seems very plausible that this kind of thing could be an accidental error; I don't know if there is any good evidence for a short vowel actually being possible in the first syllable of staturus.
sŏnātūrus from sŏno, sŏnāre/sŏnĕre, sŏnŭi, sŏnĭtus (J.R., p. 43)
- jŭvātūrus from jŭvo, jŭvāre, jūvi, jūtum (Leonard, p. 51).
However, Peter Bullions (1867) and Albert Harkness (1867) say that in compounds, jūtūrus is also used.
sĕcātūrus from sĕco, sĕcāre, sĕcuī, sectum (Leonard, p. 51).
However, Bede's De Orthographia seems to say "secturus, non secaturus".
frĭcātūrus from frĭco, frĭcāre, frĭcuī, frictum/(fricātum).
(The L&S entry says that the supine is "rarely" fricātum)
Emmanuelis Alvari E Societate Iesu Grammatica Sive Institutionum Linguae Latinae (1627) gives a long list including the following forms, but I haven't verified it yet, and some seem a bit doubtful: cubaturus, domaturus, crepaturus, vetaturus, tonaturus.
Grandgent 1907 ("An Introduction to Vulgar Latin") says that in Vulgar Latin, -ātus was extended to many past participles of first-conjugation verbs that formerly had past participles in -ĭtus: the examples given are *crepatus, domatus, plicatus, *sonatus, *tonatus, vetatus.
B. in -uitūrus, from verbs ending in -uo(r) in the present.
You already mentioned this category.
- ruitūrus vs. -rutus (Hale and Buck).
- "abnuitūrus (vs. nūtus 'the hint')" (Remberger)
- fruiturus and construiturus (Neue and Wagener)
C. in -Citūrus (C = any consonant)
nāscĭtūrus from nāscor, nascī, nātus (J.R., p. 43)
nascendus also seems to be used, but I'm not sure whether there is a difference in meaning.
moritūrus from morior, morī, mortuus.
oritūrus from orior, orīrī, ortus.
graditūrus from gradior, gradī, gressus (Neue and Wagener, p. 588).
nōscĭtūrus from nōsco, nōscĕre, nōvī, nōtus (J.R., p. 43)
Remberger mentions the prefixed form "ignoscītūrus (vs. ignōtus)".
părĭtūrus from păriō, părĕre, pĕpĕrī, partus/părĭtus.
Mentioned in brianpck's answer to "Is cultura a future participle?" and TKR's answer to "Stem for derivatives like figura, statura and cultura". Remberger says "cf. Ernout 1953".
vincitūrus from vīvō, vīvĕre, vīxī, victus (Remberger).
However, De Orthographia by Flavius Caper (or maybe in part by a Pseudo-Flavius Caper?) seems to give an analogical argument in favor of using victurus instead of vinciturus, which suggests that there may have been some degree of confusion during the time of the author (although I guess the regular form mentioned here could just be a hypothetical invention).
haurītūrus (Remberger) or hausurus (Johnson) from hauriō, haurīre, hausī, haustus.
gauditūrus from gaudeō, gaudēre, gāvīsus (Remberger).
Note: gavisurus does seem to exist.
E. In -Citurus, might be rare?
crēscitūrus from crēscō, crēscĕre, crēvī, crētus (Remberger).
I'm not sure where we have examples of the form crēscitūrus.
adduciturus once instead of adducturus from addūco, addūcĕre, addūxī, adductum (Johnson says the single occurrence of adduciturus is in Plautus)
cōnsequitūrus from cōnsequor, cōnsequī, cōnsecūtus (Remberger).
But Neue and Wagener, who say that consequiturus occurs in one inscription, "aus dem J. 257 n. Chr., I. Neap. 1524", suggest that it is just a mistake.
Sources for the listed participles
The books with lists of (possible) exceptions that I used to compile my list above:
Hale, William Gardner and Carl Darling Buck (1903). Latin Grammar
J.R. (1705). Rules and Rhetorick Translated for the Younger Scholars in Bury School
Johnson, Richard (1718). Grammatical Commentaries
Leonard, J Russell (written some time before 1882). A Latin grammar
Remberger, Eva-Maria. "Participles and nominal aspect", Inflection and Word Formation in Romance Languages, (2012), edited by Sascha Gaglia and Marc-Olivier Hinzelin, p. 273-274.
Neue, Christian Friedrich and Carl Wagener. 1985. Formenlehre der lateinischen Sprache, (pp. 586-590).