It was a big deal during the 1960 campaign.
Not that Nixon used it in the official campaign, but the media played it up. More in a negative light, IIRC. 1st Catholic President. IOW, first non-WASP president,. Will it work? Can he be trusted?
As for the assassination, thing with Kennedy, as with Trump, is that there were was a very strong potential of a family dynasty in the WH. Bobby was popular as AG, and Teddy hadn't hit the skids yet.
I think that's a factor that is not looked at enough. Families with a strong successor potential endanger too many political aspirations of those not connected to the family. LBJ didn't have anywhere near the star power the Kennedy boys did, for example. Very much a motive there, when theories bubbled up later linking LBJ to the assassination. Today, lord forbid Hunter gets near the WH, and there's no other Bidan's waiting in the wings, so Joes's safe.
The LBJ win over Goldwater in 1964 was, in part, due to Kennedy sympathy effect and the desire to continue the Camelot aura after the assassination, IMO. There was really no major suspicion of an LBJ involvement just a year out, it was all directed at Cuba.