Should a GFCI interrupt the entire circuit?
Yes this is correct; a GFCI will protect downstream loads.  The purpose of this is that you only need a single GFCI outlet per circuit. Alternatively you could use a GFCI breaker, but these tend to be more expensive.

If this is not behavior you want and you can confirm that it is not needed for safety and code-compliance reasons (ie: it doesn't feed any downstream bathroom, kitchen or wet/damp location outlets), you can rewire the outlet with a pigtail instead of using the Load side of the outlet - the outlet will work as a standalone outlet and trips will not affect downstream loads.