[Science and the world of tomorrow] Earth tilts to 34 deg. By some fluke, how does life on Earth change for good or bad?

Half of Scotland and Half of Canada would be within the Arctic Circle. The seasons would be much more pronounced with colder winters and hotter summers. The closer you got to the equator the less you would notice this effect. There would be more storms and they would be more powerful. It wouldn’t be good for mankind but we would survive.

Here’s nice Article on this

As @flutherother has noted, the change in weather patterns for the high northern and southern latitudes would be extreme: colder and longer winters as well as hotter and longer summers. Weather would change in ways that can’t even be predicted. Mankind would tend to move more to the tropics to avoid the extremes – just as few people currently live in the highest northern and southern latitudes already. That would become more pronounced.

The long term climate effects would be startling – and unpredictable – as well. Since there is more of the Earth’s land mass in the northern hemisphere, it’s likely that the northern summers would heat the planet’s surface dramatically, and that would have a ratcheting effect over time, I expect, because the southern winters would probably not freeze enough ice to overcome the northern summers.

Sea navigation would be difficult, as most of Europe, all of Canada and the northern ports in the USA would be icebound for their winters. Russia might become more aggressive in seeking the warm water port that it has always wanted.

But those are all long term effects and could be dealt with.

The nightmare is in your scenario that this all occurs “over a series of 3–5 months”. Crops in both hemispheres, except in the tropics (where relatively little of the world’s agriculture is done) would be devastated. There would not be time to respond to the planting and harvesting needs of the other hemisphere’s summer season to take advantage of its growing season so that it could support the extended winter in the other hemisphere. (And all of that planning would be iffy, anyway, since no one can predict what the summer weather would be like.)

In any case, whatever might occur to cause the planet to recess on its axis an additional 11–12° from vertical (relative to its plane of rotation about the Sun) would probably have already doomed most of the planet’s surface life, anyway.

This would be a mass extinction event for many species. Mankind might be one of them.