You will lose the research because it comes from your State Religion buildings, and under FR you no longer have a State Religion.
FR is one of my favourite civics. It has many benefits:
- If you're in a game with several different and conflicting religious blocks, FR can be the best diplomatic choice to get along with everybody.
- If several religions have spread to you, the extra
for cheap--one lousy missionary per city--can be very handy.
- Once you research Scientific Method the
benefit from monasteries goes away. FR's +10%
per city can often make up for that.
- It is a lower-cost civic than OR, Theocracy, or, usually, Pacifism (which has that nasty extra charge for your military).
However, as you've noticed, if you've played what I call a "religious game" (you've leveraged religious buildings and wonders (U of S, Spiral Minaret, AP, etc.), then FR is not as attractive.