Changelings are considered "shapechangers", so they're unaffected by polymorph
The description of the polymorph spell says (emphasis mine):
The spell has no effect on a shapechanger or a creature with 0 hit points.
As you note, the changeling race has a trait that allows them to change their appearance, but it has gone through a few iterations before the race was finally published in Eberron: Rising from the Last War.
Past versions from Unearthed Arcana
The version that appeared in the very first Unearthed Arcana back in 2015, UA: Eberron, had this trait be named Shapechanger; the details on how the trait worked were pretty barebones:
Shapechanger. As an action, you can polymorph into any humanoid of your size that you have seen, or back into your true form. However, your equipment does not change with you. If you die, you revert to your natural appearance.
However, Eberron content would not reappear in any official capacity until 2018, when the Wayfinder's Guide to Eberron was released as an unfinalized "living document", and then the various parts of the book (races, magic items, and eventually the artificer) went through the Unearthed Arcana process for playtesting. In the version of the changeling that appeared in UA: Races of Eberron and in that initial version of WGtE, the trait's name was changed to Change Appearance, and how it worked was explained in much more detail:
Change Appearance. As an action, you can transform your appearance or revert to your natural form. You can’t duplicate the appearance of a creature you’ve never seen, and you revert to your natural form if you die.
You decide what you look like, including your height, weight, facial features, the sound of your voice, coloration, hair length, sex, and any other distinguishing characteristics. You can make yourself appear as a member of another race, though none of your game statistics change. You also can’t appear as a creature of a different size than you, and your basic shape stays the same; if you’re bipedal, you can’t use this trait to become quadrupedal, for instance. Your clothing and other equipment don’t change in appearance, size, or shape to match your new form, requiring you to keep a few extra outfits on hand to make the most compelling disguise possible.
Even to the most astute observers, your ruse is usually indiscernible. If you rouse suspicion, or if a wary creature suspects something is amiss, you have advantage on any Charisma (Deception) check you make to avoid detection.
For this version of the race, people could only speculate whether they might be shapechangers; nothing mechanically defined them as such.
Final published version
When Eberron: Rising from the Last War was finally published in 2019 with the final version of the changeling race (and Wayfinder's Guide to Eberron updated to match), the name of the trait was changed to Shapechanger once more, but very little else was changed about the trait except to trim some unnecessary verbiage and remove the automatic advantage on Deception checks to avoid detection. The changeling's Shapechanger trait now reads (E:RftLW, p. 18) now reads:
Shapechanger. As an action, you can change your appearance and your voice. You determine the specifics of the changes, including your coloration, hair length, and sex. You can also adjust your height and weight, but not so much that your size changes. You can make yourself appear as a member of another race, though none of your game statistics change. You can’t duplicate the appearance of a creature you’ve never seen, and you must adopt a form that has the same basic arrangement of limbs that you have. Your clothing and equipment aren’t changed by this trait.
You stay in the new form until you use an action to revert to your true form or until you die.
The name of this trait would indeed suggest that changeling PCs were intended to be treated as shapechangers mechanically. If they didn't intend that to be the case, they wouldn't have renamed the racial trait from "Change Appearance" to "Shapechanger".
The NPC changeling statblock (E:RftLW, p. 317) also has the "shapechanger" tag:
Medium humanoid (changeling, shapechanger), any alignment
Taken together with the renaming of the PC changeling's racial trait to "Shapechanger", this seems like compelling evidence that changelings are intended to be considered shapechangers.
Keith Baker confirms that this is WotC's intent
Keith Baker, creator of the Eberron setting, made an FAQ post on his blog about Changelings in which he discusses a number of things: their culture, their shapeshifting, and how the world reacts to their existence. He also answers a number of questions in the comments.
One such commenter, Zomtron, asked whether the moonbeam spell would reveal a changeling's true form. Keith edited his initial answer into the main post, saying that:
The changeling racial description doesn’t clearly state that changelings have the shapeshifter [sic] subtype. However, in Chapter 6, the example changeling NPC DOES have the shapeshifter [sic] subtype, which means that it’s vulnerable to moonbeam and immune to polymorph.
However, another commenter, Nitro~Nina, replied to Zomtron's question pointing out that:
Given that the Changeling ability is called “Shapechanger”, I’d imagine that it’d be ruled that way most of the time (though I’m certainly no authority).
And I concurred with that in my reply (which points out a few of the same things I point out here):
Yes, I agree that changeling PCs would be treated as “shapechangers” mechanically – if they didn’t want that to be the case, they wouldn’t have renamed the racial trait from “Change Appearance” to “Shapechanger”. The NPC changeling having the “shapechanger” tag further supports this.
Keith Baker responded to me to confirm my assessment:
I have confirmed with WotC: Changelings ARE supposed to be considered shapechangers. As such, they are indeed immune to polymorph and vulnerable to moonbeam.
While Baker's comments on his own blog posts are not technically a source of official rulings, I think he is a reliable enough source to consider this a communication of designer intent.
Jeremy Crawford also unofficially confirms this
Getting a bit self-referential here... ThinkDM referenced and linked to this very answer in this December 2019 tweet. Rules designer Jeremy Crawford retweeted it and added the following comment:
In Eberron, changelings have the Shapechanger trait. That means a changeling is, indeed, a shapechanger.
Although Crawford's tweets are not official rulings, this provides further support for the interpretation that changelings are mechanically considered shapechangers.