We are using this module in one of our projects and so far i can really recommend it.
I did not notice the low frequency requirement and the proposed reader is using 13.56MHz. But the same company has some 125kHz readers as well, those may have similar options to exclude specific transponder types. Depending on the requirements, it could also be an option to "filter" specific reader types in software as soon as a tag is detected.
I am not sure if this is what you need, but you can configure the module to exclude specific transponder types from the transponder search.
Don’t search for ISO14443A transponders
Don’t search for ISO14443B transponders
Don’t search for PicoPass / ICLASS transponders
Don’t search for SRX transponders
Don’t search for ISO15693 transponders
FYI, the following transponder types are supported:
00 Mifare® Mini
01 Mifare® Classic 1K
02 Mifare® Classic 4K
03 Mifare® Plus S
04 Mifare® Plus X
05 Mifare® Ultralight / Ultralight C
06 Mifare® DESFire
0F Unknown ISO14443A transponder
10 I•Code SL2
11 I•Code SL2-S
12 Tag-it™ HF-I Plus Inlay
13 Tag-it™ HF-I Plus Chip
14 Tag-it™ HF-I Standard
15 Tag-it™ HF-I Pro
16 ST 24LR16 Dual Interface EEPROM
17 ST 24LR64 Dual Interface EEPROM
18 Fujitsu MB89R118
19 Fujitsu MB89R119
1F Unknown ISO15693 transponder
30 Picopass / ICLASS transponder
40 SRX transponder
80 ISO14443B transponder
Following my link, there is a PDF with technical specifications available, but you have to contact their support for the extensive technical handbook.