Note: this is very, very likely to be intended, even considering this has been triaged, due to it being an explicit option in model files. This is further reinforced by the fixing of MC-48831.
Cross models' constituent pixels are rectangular, where square pixels would be expected for consistency with all other models. This is also a parity issue. Likely intentional though.
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Can confirm in 21w05b.
Can confirm in 21w06a.

In 21w08a
This is intentional. It's literally specified in the model:
"rotation": {
"origin": [ 8, 8, 8 ],
"axis": "y",
"angle": 45,
"rescale": true // <----------
}
The rescale property tells Minecraft to stretch te texture. If set to false, the texture will not be stretched. This property is set to true deliberately though: setting it to false makes the cross model look weird and thin.
Can confirm in 21w11a.
Relates to MC-214078.
Can confirm in 21w13a.
This makes me wonder how the cross models would look like unstretched.
Can confirm in 21w16a.
Can confirm in 1.17.

Can confirm in 1.17.1 Release Candidate 2.

Can confirm in 1.17.1.

Can confirm in 21w39a. Also affects cave vines.

Can confirm in 21w40a.

Can confirm in 21w42a.

This is WAI, as it looks far better in-game. Do note that Bedrock attempted to fix this bug, resulting in very odd looking cross models in-game that look too small.

Can confirm in 1.18 Pre-release 2.
Can confirm in 1.18.
Can confirm in 1.19 and 1.19.1 Pre-release 1.
Can confirm in 1.19.2.
Can confirm in 1.19.3.

Affects 1.21

For certain blocks, this stretching is absolutely necessary. Pumpkin and Melon Stems would not connect to the blocks properly if they were not stretched. Cobwebs also rely on the stretched model to avoid a "floating" appearance.

Since https://bugs.mojang.com/browse/MCPE-188479 (the Bedrock equivalent of this report) was fixed in 1.21.70 by adding stretched cross models to Bedrock, this report should be marked Works As Intended.
Can confirm.