I don’t think that would be a big problem. Hey, if JFK could do it, so could Jindal.
You are forgetting one important factor: JFK was a Democrat. Traditionally the majority of Catholics vote Democrat. Just because Jindal is Catholic does not mean that Catholics will vote for him.
(Kennedys have evidently been able to do that for some time.)
I hope Jindal can't, and won't, say that.
The traditional nativist slam on Catholics is that their real loyalty is to a foreign power. (The Vatican is of course a grave threat to US interests; why, it's almost big enough to walk a large dog. ;-))
(This comes straight out of the Reformation-era polemic in England; look up Regnans in excelsis and the English response to it, Guy Fawkes Day, etc.)
Kennedy defused that by throwing his faith under the bus. If Jindal is half the man I think he is, his Catholicism is a non-negotiable part of who he is ... as mine is of me.
If you're looking for a man of integrity and strong Christian convictions, with Catholicism being an inextricable part of both, then I hope we can unite behind Governor Jindal.