Bash 4+, 77 bytes

Replaces first char of the first (non-empty) input string with 1,2,3 until no match is found to either input. Try it Online!

-9, -12, -9, -8 bytes all thanks to GammaFunction

x="${1:-$2}"
for s in {1..3}"${x:1}"
{ [[ $s = @($1|$2) ]]||break;}
echo "$s"

(quite an improvement over the original...)

Bash, 115 .. 77 bytes

Replaces first char of the first (non-empty) input string with 1,2,3 until no match is found to either input. Try it Online!

-9, -12, -9, -8 bytes all thanks to GammaFunction

x="${1:-$2}"
for s in {1..3}"${x:1}"
{ [[ $s = @($1|$2) ]]||break;}
echo "$s"

(quite an improvement over the original...)

Bash 4+, 85 bytes

Replaces first char of the first (non-empty) input string with 1,2,3 until no match is found to either input

• saved 9 bytes thanks to ideas from GammaFunction
• saved another 12 bytes using more string shenanigans by GammaFunction
• chopped another 9 due to Gamma's obscure excellent bashisms :)

x="${1:1}"
for((;i++<4;)){
o=$i${x:-${2:1}}
[[ $o = @($1|$2) ]]||{ echo "$o";exit;}
}

Try it Online!

(quite an improvement over the original...)

Bash 4+, 77 bytes

Replaces first char of the first (non-empty) input string with 1,2,3 until no match is found to either input. Try it Online!

-9, -12, -9, -8 bytes all thanks to GammaFunction

x="${1:-$2}"
for s in {1..3}"${x:1}"
{ [[ $s = @($1|$2) ]]||break;}
echo "$s"

(quite an improvement over the original...)

Bash 4+, 85 bytes

Replaces first char of the first (non-empty) input string with 1,2,3 until no match is found to either input

• saved 9 bytes thanks to ideas from GammaFunction
• saved another 12 bytes using more string shenanigans by GammaFunction
• chopped another 9 due to Gamma's obscure bashisms :)

x="${1:1}"
for((;i++<4;)){
o=$i${x:-${2:1}}
[[ $o = @($1|$2) ]]||{ echo "$o";exit;}
}

Try it Online!

Bash 4+, 85 bytes

Replaces first char of the first (non-empty) input string with 1,2,3 until no match is found to either input

• saved 9 bytes thanks to ideas from GammaFunction
• saved another 12 bytes using more string shenanigans by GammaFunction
• chopped another 9 due to Gamma's obscure excellent bashisms :)

x="${1:1}"
for((;i++<4;)){
o=$i${x:-${2:1}}
[[ $o = @($1|$2) ]]||{ echo "$o";exit;}
}

Try it Online!

(quite an improvement over the original...)