My local ISP says that they have to mount theirs own ONT devices and refusing me to connect my FTTH GPON/ONU (I have Mikrotik SFP GPON/ONU) because "It won't authorize on other companies devices". They mount some Huawei router. Is it possible?

If the ISP says no, then no.

Sure there may be technical compatibilities - but more goes into it then that. Their provisioning and other network tools may be based around using their own GPON device (GPON on NBNCo in Australia, the national network, requires their ONU for provisioning and then handed off via ethernet).

So in short - if ISP says no it will be a no. THey likely have it ACL'd and would have to be paid a lot or very well convinced to let you go against standard policy.

There is a possibility, that you can overcome it, but not with mikrotik ONT for sure.
Try searching the forum - there is a large thread about suitable ONTs in SFP form-factor and the overall procedure.
Might be possible with your ISP, might be not.
Keep in mind that you will still need to get a device that your ISP is giving you - in order to clone S/N and PLOAM from it into your device.