Hi James,
Great question. I think it's important to note John spoke of confessing our sins in 1 John 1:9 and that if we say no sin is in us we deceive ourselves 1 John 1:8.
Hence, the battle with the flesh is ongoing.
As mentioned, we are saved by grace through faith (Eph. 2:8-9) and saved by faith without works of the law (Rom. 4:3-4).
When it comes to justifying our faith before man or showing fruits over time loving other is no doubt a fruit expected to come with the Spirit's power (fleshly war continues of course).
We love God because he first loved us (1 John 4:19)- God's grace shapes our hearts and makes it possible.
As such I would say loving others in an inextricable part of working out our salvation (Phil. 2:12-13) through the sanctification process. Remember, we are saved (by grace through faith), yet being saved through the transformation in the sanctification process.
It is ultimately an order issue- grace through faith comes first, works follow. The battle has been won on the cross yet is also being played out daily in the flesh v Spirit.
These are some quick thoughts- hope it makes sense.