The point is likely to avoid branch mispredictions, in addition to having the result as 1 or 0 instead of true or false (allowing follow ups as bitwise operations).
Compare how this compiles:
var a, b, c, d byte
_ = a == b && c == d
=>
0017 (foo.go:15) MOVQ $0,BX
0018 (foo.go:15) MOVQ $0,DX
0019 (foo.go:15) MOVQ $0,CX
0020 (foo.go:15) MOVQ $0,AX
0021 (foo.go:16) JMP ,24
0022 (foo.go:16) MOVQ $1,AX
0023 (foo.go:16) JMP ,30
0024 (foo.go:16) CMPB BX,DX
0025 (foo.go:16) JNE ,29
0026 (foo.go:16) CMPB CX,AX
0027 (foo.go:16) JNE ,29
0028 (foo.go:16) JMP ,22
0029 (foo.go:16) MOVQ $0,AX
With this:
var a, b, c, d byte
_ = subtle.ConstantTimeByteEq(a, b) & subtle.ConstantTimeByteEq(c, d)
=>
0018 (foo.go:15) MOVQ $0,DX
0019 (foo.go:15) MOVQ $0,AX
0020 (foo.go:15) MOVQ $0,DI
0021 (foo.go:15) MOVQ $0,SI
0022 (foo.go:16) XORQ AX,DX
0023 (foo.go:16) XORQ $-1,DX
0024 (foo.go:16) MOVQ DX,BX
0025 (foo.go:16) SHRB $4,BX
0026 (foo.go:16) ANDQ BX,DX
0027 (foo.go:16) MOVQ DX,BX
0028 (foo.go:16) SHRB $2,BX
0029 (foo.go:16) ANDQ BX,DX
0030 (foo.go:16) MOVQ DX,AX
0031 (foo.go:16) SHRB $1,DX
0032 (foo.go:16) ANDQ DX,AX
0033 (foo.go:16) MOVBQZX AX,DX
0034 (foo.go:16) MOVQ DI,BX
0035 (foo.go:16) XORQ SI,BX
0036 (foo.go:16) XORQ $-1,BX
0037 (foo.go:16) MOVQ BX,AX
0038 (foo.go:16) SHRB $4,BX
0039 (foo.go:16) ANDQ BX,AX
0040 (foo.go:16) MOVQ AX,BX
0041 (foo.go:16) SHRB $2,BX
0042 (foo.go:16) ANDQ BX,AX
0043 (foo.go:16) MOVQ AX,BX
0044 (foo.go:16) SHRB $1,BX
0045 (foo.go:16) ANDQ BX,AX
0046 (foo.go:16) MOVBQZX AX,BX
Although the latter version is longer, it's also linear -- there are no branches.