In the following sentence, the parallel construction of the infinitives "to acknowledge" and "to accept" have, at least temporarily, befuddled me

Taking bracketed adjunct and supplement out of the first sentence given

To acknowledge the equality of black folks

would [also],

[so it was believed],

accept a lowered status for rural whites.

we have:

To acknowledge the equality of black folks would accept a lowered status for rural whites.

simplify with demonstratives and take out the auxiliary:

To acknowledge this accepts that

so, in grammatical terms the question would be:

Is a to-infinitival subject allowed for the verb accept?

There is at least one other example of a similar construction out in the wild:

To hold otherwise would accept that the parties were diligent enough to account for whatever inflation may exist up until the lease began, but, for no understandable reason, completely ignored the decades of inflation that would occur after the lease began.

Hardin St. Marine LLC v. Kenova Terminal Co., CIVIL ACTION NO. 3:18-1181, 7 (S.D.W. Va. May. 22, 2019)

For the second sentence:

To acknowledge the equality of black folks would be to accept a lowered status for rural whites.

Simplified:

To acknowledge this is to accept that.

The structure here is:

[to-infinitival] be [to-infinitival]

This structure is fairly common and seems like the clear choice between the two.

Group X was loath to acknowledge the equality of black people since, they believed, doing so would lead to a lowered status for rural whites.