This is related to D691#13273. Once we have all necessary FMN rules defined, we can create a pre-defined filter, which will appear in FMN for all Fedora users, and will be enabled by default. It would be something like this:

Title: Taskotron release-critical check results for packages that I own
Rule: A particular user's packages (any acl)
    Param: fasnick
Rule: Release-critical taskotron checks
Rule: Taskotron task failed or changed outcome

I don't know where default FMN filters are defined, but our FMN rules live here, if that helps a little:
https://github.com/fedora-infra/fmn.rules/blob/develop/fmn/rules/taskotron.py

Please make sure this really appears at FMN for all existing users (without the need of resetting everything to default).

We would probably need a similar filter also for Bodhi updates, but I don't currently see any filter that would allow us to filter those, something like //A particular user's updates//. Investigate what we need to do about that and file a new ticket.