In 5e, seemingly all races know "Common and [at least 1 other language]" for their languages.
Are there player races or subraces published by Wizards of the Coast, either officially or in UA, that do not speak common?
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All official player races in D&D that have been published in books so far speak common, because that is simply the way you're expected to communicate with eachother during the game. All the current sourcebooks that add races have them knowing and speaking common and that is unlikely to ever change; there is only one exception, and that is a technicality.
Kenku understand common and they can pronounce common words, but they can't actually 'speak' common, because they lack the ability to speak. Their ability to be creative was taken away from them, and as a result, so was their ability to speak. They now mimic things other people have said to them and the sounds of things around themselves to get their ideas across. (Which is, ironically, a very creative way of solving the communication problem for a race with no creativity, but eh, their lore is weird already.)
Planeshift:Ixalan includes optional rules for not everyone speaking Common. When using these rules, the merfolk, human, vampire, orc, and goblin subraces presented therein do not speak common, and neither does the new-to-that-material siren race.
Because they can't speak at all. They can read it and understand it, though.
Grugach, from the Elf Subraces UA, only speak Sylvan.
Grung, from the 2017 Extra Life charity stream, are even more limited and only speak Grung.
WotC only uses the term 'official' sparingly. It comes up a lot because it's used in the UA boilerplate:
This is Playtest Material
The material here is presented for playtesting and to
spark your imagination. These game mechanics are in
draft form, usable in your campaign but not refined by
final game design and editing. They aren’t officially part
of the game and aren’t permitted in D&D Adventurers League events. If we decide to make this material official, it will be
refined based on your feedback, and then it will appear
in a D&D book.
That boilerplate makes it sound like there are two groups of material, 'official' and 'unofficial' material, and there are clear rules about what goes where. This is not the case. In actuality, very few books include self-labeling or marketing as 'official'-- the PHB does, but, for example, Xanathar's Guide to Everything doesn't and hasn't had any ads run that way (at least that I've seen-- it's difficult to be certain in the age of digital marketing). Instead, there are layers of canon as typical for D&D games, where different groups make sets of different component materials and several competing sets lay claim to the 'official material only' term. Is Planeshift official? They are published with a different disclaimer, one that avoids that language, and published officially by WotC e.g. on DM's Guild. Mike Mearls says no, though, and they aren't sold as physical copies.
Are livestream things official? The WotC website sure seems to think so. Dndbeyond doesn't, though.
Ultimately, what you have to come to terms with is that the designers haven't put a lot of stock into the idea of 'official' content. There's a clear distinction between AL-legal and not-AL-legal sources, but beyond that everything is a lot fuzzier. I've chosen to use a very big-tent approach to the definition of official in answering this question. You might disagree with some or all of the races listed counting as official, but hopefully you can understand how someone else might see that very same game content as an official WotC product.
As kenku (Volo's Guide to Monsters, p. 109) don't speak at all, they don't speak common either.
Published in UA and not carried forward to Mordenkainen's Tome of Foes unlike other options in the same article, Grugach Elves have a languages trait which excludes common:
Languages. Unlike other elves, you don’t speak, read, or write Common. You instead speak, read, and write Sylvan.
While published by WotC, One Grung Below is not offical, nor UA, but a charity supplement for Extra Life. The grung playable race included does not speak common. (Credits to V2Blast for the find)