What's the "opposite" of "any more"?

Solution 1:

The construction is unimportant ... any more is not generally accepted. As noted in wiktionary (and amplified in answers to the question What are the possible meanings of positive any more Peter Shor mentioned), any more is used:

1. In negative or interrogative constructions: from a given time onwards; longer, again. (eg) They don't make repairable radios any more.
2. (colloquial, chiefly Northern Ireland, US) In positive constructions: now, from now on. (eg) ‘Quite absurd,’ he said. ‘Suffering bores me, any more.’ (DH Lawrence, Women in Love)

To retain the slight sense of change in your original example, one can replace is with has become near the beginning of the sentence:

This has become unimportant for the younger generation.

You can use now as previously suggested ("This is unimportant for the younger generation now"), but note that unless a contrast has been made, now appears superfluous; the present-tense statement "This is unimportant for the younger generation" will have the nearly same meaning.

Solution 2:

I think your second sentence would be better written as:

[This] is unimportant for the younger generation now [and going forward].

If you can change the sentence structure a bit more, you could say

[This] has become unimportant for the younger generation.

or

[This] is now unimportant for the younger generation.

Solution 3:

Your second sentence is a use of "positive any more", and is fine in some regional American dialects, but is generally not allowed in standard English. I don't know of another expression you could easily replace it by — this is probably why these dialects started using it.