It easily meshes. A changeling with no powers is a pure mortal with a Fey parent. Just because you fit the musts for a template (in the case of changelings having a Fey parent) does not mean you must take that template.
No, a Changeling with no powers is a half mortal who has the powers of fairy running through their veins. Their powers can increase in a heartbeat. As the template says, that's the point.
Just as the write up for Pure Mortal template says that Pure Mortals have nothing supernatural going on.
That's the RAW. That's Jim's setting as written. You are welcome to change it for your game, but that involves homebrew rules.
If you want a custom Template, I'd say
Template: Unaware Changeling.
Synopses: You're Meryl before she had to pull that tractor off of her half-brother. You have the blood of the Fae running through your veins, allowing instant access to certain powers (work out with the GM what these powers are; in all cases they should be based on the powers that your non-human parent possesses). Since you are ignorant of your heritage, you cannot choose mortality (i.e. you cannot renounce your heritage in ignorance).
Musts: No powers (allowing you +2 refresh bonus as a variant of Pure Mortal. Note that this bonus will vanish when you activate your first power and switch to the Changeling Template. If this causes your current Refresh level to drop below 1, you become an NPC.
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There. A short, homebrew template that fits what you are looking for.
Richard