It was always about communication. The single deadliest blow that was ever stricken to the existing rich dialect continuums was mass media (newspapers, and later broadcasting). Where before you had populations relatively isolated across a wide geographic area, only conferring with their immediate neighbors, now you had something that would reach all the way to the political border (and beyond). The second blow was the public school system, that usually standardized on a single literary standard country-wide.

In the age where importance of geography is diminished, and with so many channels of communication for both text and voice, a trend towards a single language seems inevitable - there are just too many things that would benefit from it, from science to commerce, and to some extent even art (you trade diversity for audience).

Actually, the impact that standardized language education has had on dialect variation isn't quite clear. It appears to have had some impact, but not as much as laypeople usually think. In fact, standard written American-English has undergone quite a few changes over the last 100 years and things that were non-standard have become standard. Likewise with mass media. There is no evidence that mass media has had any effect on the rate of linguistic change and variation in America. The biggest impact has probably been the increase in ease and speed of modern transportation. Regardless, there is likely more dialect variation in America today than there was 1-200 years ago, though geographic variation may be slightly diminishing (at least intraregionally) and socioeconomic variation may be more important.

The biggest factor in dialect development is time, which is why you see a large variety of dialects in England as compared to the USA. England is much smaller, but has had much longer for dialects to develop.

Does it mean, then, that as the people who are anti-immigration such as Donald Trump get elected and geographic mobility (potentially) decreases, we can work our way backwards and say that these languages are less likely to die? In other words, does the trend towards anti-globalization lead to the unexpected side effect that some languages may actually take longer to die?

Yes.

And it might mean some people get the chance to improve their own countries too, instead of being forced to immigrate (by globalization pressures) and try their luck on another.

Yes, but it would hardly be unexpected, and though this gets into iffy and boring questions around definitions, I don't think it's a side-effect either.