Conflict of interest = something you are directly involved with at work, or potentially worked on for the company previously. For example, if you're on the SQL Server team then contributing to SQLLite would reasonably be considered a conflict of interest, but contributions to the Linux kernel wouldn't be.

Even if your company works on a direct competitor to Linux?

By asking?

This. I have it in my contracts or a rider if they don't like amending the contract itself. I write code, when I stop working for you for the day I still write code. Yes it's lucky that I can get paid to do the main thing I enjoy, but you aren't paying me for the stuff I do off the clock. I will let you know about any major pieces of software I write (not like twenty line Python scripts for managing my music) and if you detect a conflict that's the moment to object, if you do then I'll work on something else, otherwise I own it outright and that's fair.

Good employers don't want to abuse you, and in turn don't want to get abused, drawing a line is something they can understand and their lawyers can get their heads around. "This is mine, this is yours".