Does filling your reputation bar with paragon prevent you from filling it with renegade?

Yes your bar will update accordingly.

It's because even though it's hidden, you actually have points (like 100 paragon points etc.) and the bar is just the ratio of Paragon:Renegade:Neutral (the neutral part doesn't appear on the bar, just increases its size).

So you might end a game with 1000 paragon points and 100 renegade points.

Starting a new game plus will keep those scores. If you then finish the game gaining 1000 renegade and 100 paragon, you'll have 1100 of each and be split perfectly.

You only have 1 reputation bar, and it is used for both paragon and renegade checks. Some of it will be red and some of it will be blue, the ratio will be different depending on which type of reputation you acquire more. If your bar is maxed out, only the ratio will change when you gain paragon/renegade points.

You will have more success while charming/intimidating with a full reputation bar, regardless of whether you're predominantly paragon or renegade. Some interrupts, however, are determined by which (paragon/renegade) reputation is higher, so your Shepard me be more of a pacifict than you'd like if your second playthrough is renegade, but your first was paragon.

You can change the ratio of Renegade to Paragon. I maxed my bar as 99% Paragon in a first playthrough and I've been playing a New Game + as Renegade, my bar is now at 20% Renegade and I've just reached Tuchanka.

You do keep your full rep bar, and the + neural rep opportunities maintain your rep bar's current ratio, but Paragon/Renegade points will change the balance. Just do every Renegade Interrupt (they still appear even if you're pure paragon) and every Renegade dialog option and you should see your Renegade bar rise.