There are some creatures in the plot of ToA that my players will interact with.

The problem is that their stat block says they speak only their specific language, which my players' characters don't speak.

They're Frost Giants, who normally speak only the Giant language

Is it possible for them to speak Common? Would I break some hidden or future plot point if I allow these creatures to speak Common in my ToA campaign?

Winter Wolves can translate, if desired

It is indeed possible for a Frost Giant to learn common (example: Harshnag from the Storm King's Thunder adventure)

Also, I've read ToA completely, and found no instance where allowing some giants to know common will break a plot point. Conversely: plot points might be missed if the PCs cannot communicate with the Frost Giants.

The adventure seems to indicate that the Frost Giants will converse with the PCs (with no mention that this will be in a language the PCs are unlikely to understand). Since this is presented as an intentional part of the scenario, it seems like the writers likely intended for at least one of the Giants (especially Drufi, the leader) to speak Common.

Example - ToA p.64 says:

Any character who succeeds on a DC 10 Wisdom (Insight) check quickly recognizes that Drufi's clumsy questions are...

It does not mention needing to know Giant to make this roll. Other statements include

she'll try to ferret out what, if anything, the characters know about... (ToA p.64)

If they admit they've met him but can't (or won't) tell Drufi where he is, she has all the reason she needs to capture the characters and torture the information out of them. (ToA p.64)

... they might help characters who can provide useful information. They immediately attack characters who withhold information ... (ToA p.200)

Regardless, their winter wolves speak both Common and Giant, so they could serve as translators if you decide that none of the Giants speak common (ToA doesn't mention this, so it doesn't seem like the writers intended it, but it's there in the Winter Wolf Stat block...).

Both by RAW and Probably Intention They Normally Cannot

Obviously the Stat Block says what the Stat Block says. However we can find a bit more possible evidence of intention in the introduction to another official module (flagged as spoiler because we are trying to hide the creature, not because it is a spoiler for the other module):

We can look at the very first paragraph of the introduction to the Storm King's Thunder module, which shared some of the same design team.

On page 7 it says:

Because giants figure prominently in the story, at least one character
should be able to speak and understand the Giant language.

Obviously this is not a definitive statement on the subject, but it indicates that WotC (or at least someone there) intends for the monolingual limitations of this creature to at least sometimes provide actual encounter or story challenges. This is an assumed game mechanic mentioned in the very first paragraph of this other official WotC module, so it is probably more likely to be an indication of general WotC philosophy towards this creature's linguistic skills interacting with players as anything we are going to get.

Changing This is Very Unlikely to Break Your Game

Only a very poorly designed module would require not being able to communicate with a creature such as this one.

This is because some player characters will actually speak this creature's language, either as a language they chose in character creation or as a racial ability. If the party not being able to communicate with them was central to the adventure then this would be a serious oversight. Similarly there are magic abilities which allow various sorts of communication through unknown languages, which once again is going to potentially break anything which hinges on them not speaking common.

In the end it is the DM's choice. It eliminates a potential limitation for some parties, but it is a limitation that would frequently be absent anyway, so it can hardly break any well designed module. It is likely an intentional limitation, but not necessarily one you are interested in featuring.

They do not speak Common. It would have ramifications on a plotline.

See their Stat Block:

Languages: Giant

You would currently break the methods that solve the encounter by providing a solution that

reveals intentions of the Frost Giants if the Winter Wolves aren't present (because you tried to separate the Giants from the Wolves or similar approaches).

The ramifications of this are that you would not be able to

gather information about the Ring of Winter that the giants seek.

Choosing to grant the creatures the Common language may quickly solve the aspect of an ambush by a murder-hobo party or similar threats which would result in

a combat encounter instead of a social encounter.

On the behaviour and interaction, see ToA page 64-65:

of combat or social encounter.

This doesn't break the entire campaign, but the encounter as written and changes the option for your players. Perhaps even limiting their agency if poorly played out.