Do you need to care?
As per Chekhov's Gun: only make it a problem, if you need it to be a problem. Only mention side-effects, if you intend to do something with them.
If not, if it is mentioned only for "realism", then do not. Ignore, or hand-wave it away, because all you are doing is spending the reader's time on dealing with a dead end.
"But I do want to care, I want there to be issues"
Then invent whatever issues you need for the story, either as plot devices, or as flavouring ‒ do not ignore flavour for your world, but think "spices" ‒ use to enhance the main taste, not to overpower it.
When it comes to suspended animation, there is an endless palette of possible side effects to choose from to inject into the story.
Physiological effects
- Memory loss
- Muscle atrophy
- Immunity issues
- Gastrointestinal dysfunction
- Sterility, temporary or permanent
- Allergies to new immuno-irritants
- DNA degeneration, from radiation and/or thermal motion
- Impaired motor functions, fine-motor skills in particular
- Lack of space travel experience (hellooo space motion sickness!)
Psychological effects
- Identity lag
- Culture shock
- Survivor's guilt
- Lack of peers / dead loved ones
- Ethical and moral vertigo/disconnect
- Obsolescence, skills and knowledge hopelessly outdated
...and more
Pick and choose whatever you want, because no matter what that is, you can always find a way to crowbar their presence ‒ or absence ‒ into the story.
Author decides
Willing Suspension of Disbelief is not(!) about realism, but making things credible.
Unless you are going for extremely "hard" sci-fi, remember: you are the autocrat of your story, the supreme dictator... whatever you say will happen, happens.
You do not need worry about respecting reality.
All you need consider is: can I sell this to the reader?
Realism makes it easier to achieve credibility, but things like Star Wars shows that realism is not at all necessary.
A word on works inspired by others
Note, I am not a lawyer, this is not legal advice.
Straight up use of third-party worlds is frowned upon on Worldbuilding SE, because that ‒ usually ‒ results in copyright violations, and the questions become more about canon rather than helping to develop the author's own world.
However...
Copyright protects expression, not ideas.
Concepts and themes are (usually) not copyrightable.
What this means is that whatever made it onto paper is what is protectable, not the thoughts that made things end up on paper.
Copyrightable elements are...
- Identifiable characters, meaning a totality of looks, mannerisms, name(s), backstory and similar
- Identifiable, unique plot elements
- Unique world mechanics
- Unique names/terms/jargon
This is why, for instance, Eragon does not fall afoul copyright against Star Wars: A New Hope, despite the plot being a blow-by-blow copy.
So in your case, this would mean you avoid names and descriptions that makes the reader say "Okay, that's obviously Pandora and Na'vis." or "Totally Colonial Marines... you stole that straight off of Cameron".
Avoid running into that, and you can write to your heart's content.