A similar issue with art brushes:
https://illustrator.uservoice.com/forums/333657/suggestions/51599522

I finally figured out it was the stroke that was making the group seem incorrect. Thanks for confimring.

Grouped items are supposed to interact as one item when using the Reflect or Transform tools. Now, despite being grouped. All items are impacted individually. NOTE: I am NOT using the "transform each" option.

EDIT: I see now that it's just the stroke setting that's not transforming properly. Confusing.

上下のバランスが異なる線幅プロファイルを適用したオブジェクトに対してリフレクトツールで反転処理を行っても完全な鏡像が得られない。

Step to reproduce

1. ドキュメント上に１本の線を配置する。
2. 線に対して上下のバランスが異なる線幅プロファイルを適用する。
3. リフレクトツールで左右を反転する。
4. 線自体は反転されるが、線幅プロファイルが反転されない為に完全な鏡像鏡像が得られない。

期待する結果
完全な鏡像が得られる。

実際の結果
線幅プロファイルが反転されないために完全な鏡像とはならない。

代替手段
反転したパスの線幅プロファイルに対して軸を基準に反転を適用する。

[EN]
Applying the Reflect tool to an object with a profiled stroke that has different top and bottom balances does not produce a perfect mirror image.

Steps to reproduce

1. Place a single stroke on the document.
2. Apply a stroke profile with different top and bottom balances to the stroke.
3. Use the Reflect tool to flip the stroke horizontally.
4. The stroke itself is reflected, but the stroke profile is not reflected, resulting in an imperfect mirror image.

Expected result
A perfect mirror image is obtained.

Actual result
The stroke profile is not reflected, resulting in an imperfect mirror image.

Workaround
Apply "Flip Across" in the stroke panel to reflect stroke profile.

Please refer attached file.

This is not how it behaves for me when I test it.
I try Flip Horizontally from the Transform panel’s menu, I try Reflect tool, I try Repeat > Mirror, Transform effect, Free Transform tool... each of these correctly change the direction as well!
Can you show exactly how do you do it, on video?

When Reflecting (mirroring, flipping) Paths with a non non uniform Stroke Widths, the result is not correct, since the Path direction is not reversed. (see screenshot)

If this is made with not only respecting just variable strokes, but also with Use Preview Bounds option respected, I think it should NOT toggle the actual option. Currently Ai sees toggling similar options (like Scale Strokes and Effects) in various dialog as global options, and I kinda hate it. It leads to problems, like this one: https://illustrator.uservoice.com/forums/601447/suggestions/47601263

The original idea by Johan Perjus, from https://medium.com/design-bootcamp/things-i-wish-adobe-would-address-with-adobe-illustrator-4796a89e1bae

Notice how the thicker stroke width moves to the outside of the circle when using the reflect tool, meaning that the reflect tool currently does not take the stroke width in consideration when performing a reflect (or mirror). One therefore have to manually edit the stroke width after using the tool in order to achieve a truly reflected version of the object.

Joshua, as a workaround try to apply Transform effect to the group. If it won’t help, try applying the Outline Stroke or the Outline Object effect to the group before Transform.