Overview
BID shares some structural similarities with certain membrane-translocating bacterial toxin domains such as the transmembrane domain of the diphtheria toxin (1XDT). This toxin forms a pore in the plasma membrane, consequently leading to the death of the permeabilised cell [1].
Here are the FASTA files of the toxin, 1XDT, and 2BID.

FASTA
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GADDVVDSSKSFVMENFSSYHGTKPGYVDSIQKGIQKPKSGTQGNYDDDWKGFYSTDNKYDAAGYSVDNENPLSGKAGGVVKVTYPGLTKVLALKVDNAETIKKELGLSLTEPLMEQVGTEEFIKRFGDGASRVVLSLPFAEGSSSVEYINNWEQAKALSVELEINFETRGKRGQDAMYEYMAQACAGNRVRRSVGSSLSCINLDWDVIRDKTKTKIESLKEHGPIKNKMSESPNKTVSEEKAKQYLEEFHQTALEHPELSELKTVTGTNPVFAGANYAAWAVNVAQVIDSETADNLEKTTAALSILPGIGSVMGIADGAVHHNTEEIVAQSIALSSLMVAQAIPLVGELVDIGFAAYNFVESIINLFQVVHNSYNRPAYSPGHKTQPFLHDGYAVSWNTVEDSIIRTGFQGESGHDIKITAENTPLPIAGVLLPTIPGKLDVNKSKTHISVNGRKIRMRCRAIDGDVTFCRPKSPVYVGNGVHANLHVAFHRSSSEKIHSNEISSDSIGVLGYQKTVDHTKVNSKLSLFFEIKS
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GSMDCEVNNGSSLRDECITNLLVFGFLQSCSDNSFRRELDALGHELPVLAPQWEGYDELQTDGNRSSHSRLGRIEADSESQEDIIRNIARHLAQVGDSMDRSIPPGLVNGLALQLRNTSRSEEDRNRDLATALEQLLQAYPRDMEKEKTMLVLALLLAKKVASHTPSLLRDVFHTTVNFINQNLRTYVRSLARNGMD
MSA Results from toxin comparison

Fig.1. MSA of toxin and 2BID. The differently coloured boxes indicate the conserved domains found in all the four isoforms: Green marks the BH3-B domain, purple the tBID domain, and red the BH3 domain. 22.9% of the 2BID was conserved.
The domains do not look like they are conserved and there is no clear pattern to similar amino acids. Looking closer, it was determined that 22.9% of the toxin overlapped with Human 2BID (Fig. 1). This is considered the "twilight zone" when it comes to determining if the protein is conserved. However, it is obvious that whole regions and characteristics are not conserved (Table 1). From these results, we would hypothesise that the proteins have converged, not diverged. They may be structurally similar, i.e. have the same number of hydrophobic regions and such, but the amino acids in those regions is not the same. We compared the structure of the toxin with 2BID here.

Table 1: Toxin Comparison. Protein conservation between 2BID and 1XDT. Areas of high conservation are noted with an asterisk. Although region loop 4 shows a high percentage of conservation, marked by an asterisk, this is a very small region and therefore much more likely to have incidentally high conservation. This area is unimportant regarding function of the hydrophobic core of these proteins.