When viewed from the north and south, cross models (like many plants and cobwebs) display correctly.
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However when viewed from the east and west, the block appears mirrored.
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Does this have any impact on gameplay, or does it affect models that are made in custom resource packs?

Still happening in 1.14 all the way to the 1.15 beta

In java edition: it can be mirrored as X-crossed
In bedrock edition: It has XI cross on it.
Always not fixing. It matches java model and bedrock has simply weird model thus.

Affects 1.16.230.52
Please fix it

Custom resource packs appear to be affected

The grass texture grass is supposed to be facing one side. It probably isn't the artists intention for it took like that.

This bug has not been fixed in almost 8 years and has been there since alpha 0.9.0.

All X-shaped blocks in Java Edition, their textures look will never flip horizontally no matter which direction they are viewed from.
But in Bedrock, some textures will flip horizontally then cause axisymmetric in visual:
Grass, Fern, Flowers Except Pitcher Plants), Dead Bush, Saplings, Bamboo Spling, Corals, Amethyst Buds, Amethyst Cluster, Cobweb, Weeping Vine, Twisting Vine, Hanging Roots, Warped Roots, Crimson Roots, Nether Sprouts, (Flowering) Azalea (Bottom Model), Kelp, Campfire, Soul Campfire, Sweet Berry Bushes, Mangrove Propagule.
I noticed develpers have solved this problem in some new X-shaped blocks like Pitcher Plants, Pointed Dripstone, Cave Vines, so the blocks using outdated blockshapes and render methods, they should be updated because axisymmetric is ugly if watch the model carefully.

Great, I cannot unsee it now!

I can confirm this bug still happens and is NOT FIXED in 1.21.60.21 Preview.
All Flower Pot, Cobweb, Sugarcane, all Corals, Kelp, Bamboo Spling, Amethyst Buds, Amethyst Cluster, Weeping Vine, Twisting Vine, Hanging Roots, Nether Sprouts, Azalea (Bottom Model), Flowering Azalea (Bottom Model), Campfire, Soul Campfire and Mangrove Propagule are not fixed yet, as they are still displayed wrongly from east and west sides.

A fix has been implemented for this in one of the recent Minecraft Previews.
As Rainvay commented, a similar fix was already there for newer blocks after 1.17 that consisted of two planes together in an X shape.
However I like to point out this fix which entails rendering only one side of the plane, with one side having a flipped texture, is completely broken with ray tracing.
Instead of only one side of the plane being rendered, both sides are rendered at the same time, leading to Z-Fighting with the texture, and its mirrored self being rendered on the same plane simultaneously.
Effectively resolving the bug in vanilla graphics, and making things worse in ray tracing graphics mode. I hope this issue won't be marked as resolved, because this fixes one issue and introduces another, which is closely related.
[media]Edit, here's a detailed report:
[MCPE-189266] Double-sided cross-shaped blocks render incorrectly in ray tracing graphics mode - Mojang Studios Jira

Can confirm 1.21.60.23.
Please redirect new issues elsewhere. We have MCPE-188463 for the remaining blocks. I'm not aware of any ticket about the ray tracing issue; please make one.

This still seems to effect saplings in pots on version 1.21.62.
Affects 1.9.0.5