TL;DR: When it is at the start of a syllable, not when it is at the end of a syllable.
First, do not confuse letters with sounds. It is pointless to talk about letters.
Semivowels are glides like /w/ and /j/ that act as part of a diphthong, so in conjunction with a vowel sound. In practice, only those semivowels that precede the vowel count as a consonant, not those that follow it where they count as a vowel.
So the words wet and yet are pronounced with a consonant glide at their fronts, and this is referred to as a semivowel because they start with a consonant sound. Contrast this with cow and coy where there is no consonant property involved, so those are purely vocalic: they end in a vowel sound, not in a consonant sound.
Spelling may or may not reflect this, though, because English spelling derives at best from the sounds of English that was spoken five to nine centuries ago, not from the sounds of English today. That’s why it’s pointless to talk about letters.
You have a false premise here: there is no semivowel in the word cry, only a purely vocalic, garden variety diphthong. The y in cry /kraɪ/ represents a falling diphthong /aɪ/, whereas the one is in yes /jɛs/ is the semi-vocalic glide /j/ you’re looking for, being the first element of a rising diphthong /jɛ/. Similarly in few /fju/.
Semi-vowels are things like /w/ and /j/, and they are frequently talked about only in rising diphthongs in English where they take on a consonant character. So cow has /kaʊ/ while coward has /ˈkaʊɚd/, which can also be written /ˈkawɚd/.
Similarly the noun toe and verb tow have /tou/, which can also be written /tow/. In concrete phonetics, you may see narrow transcriptions like [tʰo̞ʊ̯].
A semivowel at the start of the rising diphthong does not usually count as part of the syllable’s rime¹ so yet /jɛt/ rhymes with bet /bɛt/. Similarly the glide in queen /kwin/, [kʰwi:n] doesn’t count for rhyming, allowing it to rhyme with seen /sin/ and machine /məˈʃin/.
However with the /ju/ diphthong, some poets prefer to include the leading semivowel, preferring to rhyme cute /kjut/ with dispute /dɪˈspjut/ instead of with words lacking that /j/ component like shoot /ʃut/. So for them the vowel is the entire diphthong /ju/ including its leading semi-vowel and not just /u/, since they’re trying to rhyme with /jut/ not just with /ut/.
- rime: (linguistics) The second part of a syllable, from the vowel on, as opposed to the onset. [Wiktionary]
Given all your examples of supposedly rhyming words (they all rhyme for me a GenAmE speaker) having different possible pronunciations, both within a dictionary and between dictionaries, leads me to believe primarily not that there is some variation in pronunciation in the GenAmE population (though there very well may be variation (but consistent) between regional accents), but rather that these dictionaries are not scientifically consistent within themselves.
Either you have discovered an substantive inconsistency among these entries or these dictionary makers have performed research on all these pronunciation as part of their preparation but are not printing the outcomes/final results of the data leading them to make distinctions that are not meaningful for actual pronunciation or hearing.
You may want to construct a diplomatically worded letter to the editor in order to discover the reasoning for these pronunciations. I wonder if it would help to show one dictionary what the other dictionaries say?
Best Answer
Usually only the following vowel letters are relevant, and only for sc, not for sch.
Main possible pronunciations of sc: /sk/, /s/ or /ʃ/
In general, "c" in "sc" follows the usual rule for "c": /s/ before "e, i, y" and /k/ before "a, o, u" (the same rule of thumb applies to "g", which is usually /dʒ/ before "e, i, y" and /g/ before "a, o, u").
The /ʃ/ in "conscious" is because of the coalescent palatalization of /sj/ to /ʃ/. We may also see palatalization of unstressed word-internal /si~sɪ/ to /ʃi~ʃɪ/ when there is another vowel following, as in fasciation, which is pronounced either as /ˌfæʃiˈeɪʃən/ or as /ˌfæsiˈeɪʃən/ according to the American Heritage Dictionary.
The identity of the preceding vowel/vowel letter is normally not relevant.
Overview of the usual pronunciations:
The rules given here have exceptions. Some exceptions are optional, while other exceptions are less optional:
Some people pronounce proboscis with /sk/, but it's also fine, or even preferable, to pronounce it with /s/.
It seems to me that fascism is almost always pronounced with /ʃ/ nowadays, probably due to influence from Italian, where sc regularly represents /ʃ/ and not /s/ before i or e in any context. Still, you can find the pronunciation with /s/ listed in a few dictionaries, like Merriam-Webster and O.E.D. Suppl. (1933) (the modern Oxford English Dictionary mentions this, but doesn't list it as a modern pronunciation).
The well-known example of sceptic (and derived words sceptical, scepticism etc.) is invariably pronounced with /sk/, although in the United States the alternative spelling "skeptic" tends to be used, which corresponds more regularly to the pronunciation.
Main possible pronunciations of sch: /sk/, /ʃ/, /stʃ/ (rarely /s/)
The pronunciation of "ch" or "sch" is a quite different matter. The range of pronunciations for "ch" without preceding "s" is covered by How do I know when a word with "ch" is pronounced hard or softly?
Basically, there is no useful rule related to vowels for the pronunciation of sch. It can be pronounced /sk/, /ʃ/, /stʃ/, /s/ or even /ʃtʃ/ depending on various factors.
The pronunciation /stʃ/ can normally only occur before a vowel and in the middle of a word, not at the start or end. It seems to only occur in contexts where the /s/ and /tʃ/ can be analyzed as belonging to separate syllables, so perhaps a more detailed transcription of this pronunciation would be /s.tʃ/.
The consonant cluster /stʃ/ is sometimes pronounced as something similar to [ʃtʃ] because of processes of assimilation. If we set aside this arguably non-phonemic phenomenon, /ʃtʃ/ is a very uncommon pronunciation of sch. Some speakers may have /ʃtʃ/ in the word borsch, a recent loanword. Collins lists the pronunciation /bɔːʃtʃ/ along with alternative pronunciations /bɔːʃ/ and /bɔːʃt/. (Of course, in American English, a rhotic vowel like [o˞] or [ɔ˞] would be used). Alternative spellings of this word include "borshch", "borscht", "borsht".
The pronunciation /s/ is very rare. As far as I know, it only occurs in one pronunciation of schism (there is also a pronunciation with /sk/), and an obsolete pronunciation of schedule.
I think that schm is always pronounced /ʃm/, and schn-, schr-, schl- are always pronounced as /ʃn, ʃr, ʃl/ when they come at the start of a word/syllable. In word-medial contexts, there are a few very rare cases where -schn- might be pronounced as /sk.n/ (or /s.n/?) in scientific vocabulary (e.g. Ischnacanthus), or where -schr- might be pronounced as /s.kr/ (e.g. dyschromatopsia).
Etymology is important: broadly speaking, "sch" is pronounced /sk/ in words from Greek and /ʃ/ in words from German. Words from French are more unpredictable ("eschew" is from French, as is "schedule"). In words from Italian, where "sch" only is used before the letters "e" and "i", "sch" is pronounced as /sk/ (e.g. scherzo) ... except for when it isn't (as in one common, but commonly criticized, pronunciation in English of the word bruschetta).