Are they generally pronounced with the same vowel in Singapore English, or not?
American and British dictionaries list them both as /ɹɛd/, but I find that I pronounce red with a less open vowel than read (although I can't quite tell exactly which). Looking on Youglish, I can find a number of videos with speakers that do pronounce them differently, and a number that don't. It's hard to find Singapore English examples on Youglish though.
As the dictionaries you've looked at indicate, in most areas, red and read (past tense) are pronounced with the exact same vowel phoneme (which we can write "/ɛ/") and are homophones. The exact phonetic quality of this vowel phoneme /ɛ/ may vary between speakers, or even from time to time with the same speaker. For example, some accents of English use a variant that is phonetically a closer/higher vowel [e], and some accents use a more backed variant, [ɜ] or [ɐ], as a pronunciation of this same vowel phoneme (the vowel found in words like dress).
In Singapore English, the category of words that dictionaries show with /ɛ/ has apparently split for many speakers into two categories, one with a higher/closer quality and one with a lower/opener quality. I cannot remember where I originally read about this, but you can see a presentation covering this phenomenon here: "The NEXT-TEXT split in Singapore English: Comparing self-report and speech production", Rebecca Lurie Starr and Amanda Choo Shimin, (National University of Singapore), presented at New Ways of Analyzing Variation 48 at the University of Oregon, October 2019.
Starr and Choo Shimin's data set includes red but not read. They indicate that survey participants in one study were fairly evenly split between reporting a raised and unraised vowel in red, while phonetic analysis of another group of speakers showed a fairly high percentage of raising (over 80%).
The presentation has a citation indicating that this is apparently not connected to the pronunciation of these words in varieties of English spoken elsewhere:
“there seems to be no straightforward way to predict which vowel some words will have on the basis of BrE or any other external variety of the language. (Deterding 2005:185)”
(page 10)
To me, as a non-speaker of Singapore English, this split is surprising and not something that I would usually think to listen for.
The higher (narrower) vowel in "red" and "next" works as a systematic variant to the extent that there are enough speakers in a locale (Singapore) who maintain this pronunciation in a certain set of words, just as the syllabic 'n' in butt'n would be a North England one compared to button pronounced as 2 syllables.
The whole discussion seems to ensue from the presumed normative of monolingual varieties broadly essentialized as 'Brit','Am' or 'Native Speaker' English. As a Singaporean by birth (now a New Yorker), my vowels shift constantly depending on whom I'm talking to and it's no big deal unless the hearing subject happens to be (again) the traditionally monolingual 'native speaker' of English who has power over my promotion, or access into an apartment building.
My humble suggestion is, Ree-lax, lah! Most people in the world (and yes, native translinguals) do very well enriching and transforming the English language.
