I've traced the first difference down to here:

https://github.com/JuliaImages/ImageFiltering.jl/blob/167611b1ade92d5d4449a6f1cf7b93fb92946a6b/src/imfilter.jl#L326C9-L326C9

With the aberrant case, this line returns Pad(:replicate, (1, 2), (3, 2)); it should be Pad(:replicate, (2, 2), (2, 2))

And further...

image = zeros(3, 3)
kernel1 = factor1, factor2 = ImageFiltering.factorkernel(Kernel.gaussian(1))
factor2a = (factor2 |> vec |> centered)'
kernel2 = (factor1, factor2a)

ImageFiltering.expand(axes(kernel1[1]), axes(kernel1[2]))
# (OffsetArrays.IdOffsetRange(values=-2:2, indices=-2:2), OffsetArrays.IdOffsetRange(values=-2:2, indices=-2:2))

ImageFiltering.expand(axes(kernel2[1]), axes(kernel2[2]))
# (OffsetArrays.IdOffsetRange(values=-1:3, indices=-1:3), OffsetArrays.IdOffsetRange(values=-2:2, indices=-2:2))

And even further:

a = centered(zeros(3))'
b = centered(zeros(3)')

axes(a)
# (Base.OneTo(1), OffsetArrays.IdOffsetRange(values=-1:1, indices=-1:1))
# axes(v::Union{LinearAlgebra.Adjoint{T, var"#s972"}, LinearAlgebra.Transpose{T, var"#s972"}} where {T, var"#s972"<:(AbstractVector)}) in LinearAlgebra at src/adjtrans.jl:298

axes(b)
# (OffsetArrays.IdOffsetRange(values=0:0, indices=0:0), OffsetArrays.IdOffsetRange(values=-1:1, indices=-1:1))
# axes(A::OffsetArrays.OffsetArray) in OffsetArrays at src/OffsetArrays.jl:295

Since the root issue is that the Julia axes function doesn't account for OffsetArrays, this is a bit awkward. Fixing this would be arguably breaking because old code may have been relying on the behavior, which is how I discovered it.

Perhaps for now, ImageFiltering could manually check for this condition and provide the correct axes. This would be a breaking release. And can add a note that it's a fix for underlying Julia behavior, and that it should be revisited once Julia contains the true fix; at a minimum to make the method conditional on the installed Julia version.

So looks like there need to be several parts to fix this:

1. Julia needs to not assume that all higher dimensions have a range of 1:1
2. OffsetArrays needs to support specifying the offset for all higher dimensions.
3. OffsetArrays.centered needs to use that feature to make an object that has 0:0 axes in all higher dimensions.

Crossref: JuliaArrays/OffsetArrays.jl#339

Since the root issue is that the Julia axes function doesn't account for OffsetArrays, this is a bit awkward. Fixing this would be arguably breaking because old code may have been relying on the behavior, which is how I discovered it.

Just because some behavior change does not necessarily make it "breaking". If a documented behavior changed, then it would definitely be breaking. However, if there is a bug, and people have been relying on that bug, but you fixed it then this is a bug fix. That said, it would be nice if you created some facilities to help people adapt to the fix if it disrupts their software.