Correct me if I'm wrong but aren't both the bunny and the eggs remnants of the spring fertility calibrations that stuck around when pagan celebrations were kinda mushed into Christian celebrations? Much like the tree wasn't originally a "Birth of Christ" symbol?
Yes, I waited until Pentecost Sunday to respond to this. I promise I won't make some joke about the Spirit moving me to respond today. Then again, I guess I already did.

There's good reason to be skeptical of claims that Christian thing X is really smuggled-in paganism, because there can be incentive on both sides to make those claims. Obviously, there's an incentive for some people to undermine Christianity by calling traditions into question, but the funny thing is that some Christians also have an ulterior motive to call those things pagan. It can be a way for some believers to be more spiritual; more pure than other Christians. There are other Christians that hear about supposed paganism, and their incentive is that it's easier to ditch the eggs or the Christmas tree than to actually do the research. (My church eschews eggs and rabbits during Easter, which I'm OK with, even though I doubt the claims of a pagan origin.)
So we have to watch out for a lack of objectivity from both sides. I can't claim to have done any exhaustive research, but I have found that for every claim of smuggled-in paganism, there is an at-least-equally valid debunking of that claim.
https://news.web.baylor.edu/news/story/2016/why-easter-was-never-anything-christian-holiday"Many religions and traditional customs have used eggs and even rabbits," Barr said. "But this doesn't mean that the Christian use of these symbols, especially eggs, is 'pagan.' Historical parallels do not equal historical evidence."
The Easter bunny was not used in Easter celebrations until the early modern world, and therefore the use of the rabbit has no historical or significant connection to any pagan festivals.
"I have seen arguments connecting Easter eggs to Babylonian and even Zoroastrian traditions," Barr said. "But the medieval European world had no knowledge of these customs or celebrations; historians didn't learn about them until very recently. The most historically logical roots for Easter eggs is their use during Medieval Easter traditions. Eggs were prohibited during Lent, and so in preparation for their return to eating eggs, people decorated eggs and used them as part of their Easter celebrations. This is the most reasonable source for the traditions we continue today."
And here is a response from our Catholic friends:
https://www.catholic.com/magazine/online-edition/no-easter-is-not-a-pagan-holiday