If Star Trek were real, would the stars/space debris seriously damage the starships?

It had “shields” but that was more of a plot device in the “technology excuse” flavor. A single hydrogen atom could destroy the enterprise at near-light speed.

That is what I figured for an “in universe” explanation.

Makes sense if applied to real life it would be destroyed. I wonder how we could prevent that. We are not advanced for that yet.

That the purpose of the deflector dish.

That is why they have navigational deflectors, to protect themselves from debris. Not sure you would even need that at warp, though, since the space with the debris would be warped around your warp bubble.

In time the windows and sensors on all Starships will erode and degrade under the bombardment of micro particles. There are few things more sad than seeing a proud ship of the line set sail for the stars only to return thirty years later as a blind and deaf hulk fit only for scrap.

As @RedDeerGuy1 and @ragingloli mentioned, they have navigational deflectors for minor debris and objects.

And as @ragingloli mentioned, the warp drives work by warping spacetime around the ship, not by accelerating it, so it’s not like they’d be hitting objects at several times the speed of light when using warp drive. But they also do use impulse engines that do accelerate the ship through space normally.

Nevertheless, it IS possible for large enough objects to be navigation hazards, as seen for example in at least one episode of the original series (e.g. at the start of “Mudd’s Women”), where the ship is speeding through an asteroid field (because it was pursuing another ship trying to lose them by doing so), in which case the shields were also used, but even so, the ship took damage and burnt out dilithium crystals. Another example, in the somewhat-differently-explained first film, has an asteroid caught in the path of the ship during warp travel and malfunctions happen, which threatens do do lots of damage.

As for Star Wars. the first (and best for taking things most seriously, IMO) film mentions navigational deflector fields as well, and the Millennium Falcon runs into and gets bumped around by debris when it arrives where the destroyed planet was.

So overall, in both cases, as in reality, yes, traveling fast makes even minor debris a serious problem wanting some sort of solution like a deflector field, and yes even with one, it can still be an issue.