From the ME wiki:
Unlike Charm and Intimidate, Shepard is not required to have any
minimum amount of Paragon or Renegade points in order for an interrupt
to be presented. All characters will encounter the interrupt at the
appropriate time, assuming they made the correct dialogue choices to
reach that interrupt as described below (if any).
Shepard always has the option to perform both kinds of interrupt. If you don't see a Paragon / Renegade interrupt, it's because there isn't one, not because of your character's reputation.
For instance, as a paragon Shepard, I was able to take the Renegade interrupts while boxing with James Vega.
What Mass Effect 3 has added is variable reputation interrupts, that change based on whether your morality leans blue or red. This does not mean, however, that you cannot perform renegade interrupts, or that you will never see renegade interrupts as a paragon Shepard - it just means that, on average, you will see more Paragon interrupts than Renegade.