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Cambridge Dictionary gives an IPA /ˈɑː.pə.zɪt/ for the word "opposite", which totally fits with what I know.
This American kindergarten teacher in the YouTube video titled: Antonym Rap: Reviewing Words with Opposite Meanings is pronouncing opposite /ˈɑː.pə.sɪt/, the difference is the pronunciation of "s" in the word.
Is it a very common and recognized way to pronounce the word "opposite"?
I think /ˈɑpəsɪt/ is not extremely uncommon, although it's a little hard for me to find sources that mention it. When I (an American English speaker) read your question, I pronounced the word both ways, and thought that while I would say it with /z/ by default, the pronunciation with /s/ doesn't sound completely impossible or unnatural to me.
The Oxford English Dictionary entry implies that American English speakers are more likely than British English speakers to use /z/, in that it gives the following list of pronunciations:
Brit. /ˈɒpəzɪt/, /ˈɒpəsɪt/, U.S. /ˈɑpəzət/
Merriam Webster suggests that the number of syllables in the word varies along with the consonant used at the start of the last syllable, but I don't think that's a complete description of the pronunciations used. I think the word is not heard with two syllables as often as it is heard with an /s/ sound.
\ ˈä-pə-zət , ˈäp-sət \
