By your question, do you mean taking a fiber connection directly via an SFP+ module, or do you meed a fiber to the home service where the ISP will supply an ONT (the consumer ones at least in the US require you to use their provided ONT, and do not harge extra for a basic ONT).
In such a case, then there are no real compatibility issues. Most FTTH providrs will use an ONT that alliws a router to get a WAN IP and other relevant configuration data via DHCP, thus they are effectively plug and play where the setup wizard does all of the work for you. In edge cases, some FTTH providers wil be jerks and add unnecessary complication such as requiring VLAN taggind and PPPoE to communicate with the ONT, thus adding like 4 additional steps and a few minutes to the setup process.
Beyond that, I don't think any of the consumer fiber providers will allow you to even use a fiber line from them directly, they often take many authentication steps to ensure that only their equipment is within the signal path, since in most locations, the optical portion is shared via beam splitters, meaning it is also easier to damage the optical equipment of others.
At the business and enterprise level, it is possible to use your own fiber transcievers with the fiber.
