Faith and repentance are gifts accompanying regeneration. In that sense, it is passive on the part of the reciplent, but not the giver (God). This is perfectly consistent with Reformed theology.
It didn't arrive by pure persuasion, though, it was implanted by the Holy Spirit. I would not ignore the fact that the gospel message is presented to the believer, but faith is still implanted through regeneration performed by the Holy Spirit.
Now, false believers can have some type of intellectual assent (even the demons have that), but they don't possess true faith. And, they won't endure. We see this in the "disciples" of John 6, who did not endure after being faced by troubling doctrines. As long as it was all about free food, they were all for it, but then they turned away after hearing difficult doctrine (a warning for the Health, Wealth, Prosperity crowd, I think).