How much could Earth's orbit shift without causing an ecological catastrophe? Seeing the news about A/2017 U1 made me wonder what would happen if a similar object, but with a mass close to Earth's, had a close call with Earth. Could it shift Earth's orbit enough to quickly and significantly change the conditions for life?

This answer sort of gets it it, but it's not clear how much of an effect the change in orbit would have.
Depending on how one defines "quickly" and "significantly," I think a gravitational influence strong enough to do that would tear apart the Earth through tidal effects long before the change in orbit would make the planet unsuitable for life.