Older transceivers will work in newer cards, but they're probably not supported. That means if there's any problem with the interface, the TAC will tell you to switch to a supported transceiver before they will troubleshoot further.
From a practical standpoint, SFP transceivers are extremely simple. The transceiver part is something called a PHY. The interface MAC talks to the PHY over a standard protocol, and there are only a few variants of this protocol (SFP, SFP+, SFP28, SFP56, SFP112, etc., depending on the SerDes rate). All SFP+ transceivers, for example, talk the same protocol to the MAC.
The transceivers also include two contacts for a low-speed serial link. On old transceivers, this just includes a link to a ROM (technically an EEPROM) which contains information like the vendor, model number, serial number, and so on. This is like the SPD ROM on a DRAM module. Some vendors use the vendor identifier here to only allow their branded transceivers to work. That's not a technical limitation, it's a marketing limitation. On more recent transceivers, this informational side-channel has been extended for "digital diagnostics monitoring" (DDM), which lets extra hardware in the transceiver monitor laser power, received light level, and so on. This information is all collected via something a bit like a LOM in a server. It doesn't interact with the operation of the transceiver, it just monitors the operation.