Honestly I can't see this happening without a POD that avoids the Baltic states being annexed by the USSR. Had these countries been just (nominally) independent *Warsaw Pact nations with decisions about immigration and legislation about citizenship made locally (even if under influence from Moscow), I could see them retaining something like the liberal attitude towards minorities these countries had in the interwar era.*
After spending 50 years under Moscow's yoke, like the majority of the Baltic people saw it, and gaining a massive Russian minority in that time, without the local native majority being asked if they accept this huge influx of immigrants, I'd say it is very hard to avoid a counter-reaction after these nations gained new independence. This especially applies to Estonia and Latvia, as mentioned above, which saw an increase in the Slavic population from 8% to 35% and 10% to 42%, respectively, between the late 30s and 1989. This growth in the size of the Russian-speaking population was enough to make the native people in these SSRs fear for their future as ethnic and cultural groups, especially as at the same time the Russian language and culture was officially and practically in a much stronger position than the native language and culture.
I guess that from a Russian POV, it might be hard to understand the members of a small ethnic and language group fearing becoming a minority in their own country, or even being wiped entirely from the face of the earth in the foreseeable future. For the Baltic local ethnic majorities, though, being a part of the USSR was a heavy ordeal, all the way from the repression and forced transfers of tens to hundreds of thousands of people in the Stalinist period. It is very hard to see the post-1990 Baltic native majorities in toto turn into practical reincarnations of Jesus Christ in their ability to turn the other cheek and to forgive their treatment under the Soviet system, or to stop fearing that the large Russian minorities are used as Moscow's catspaws to keep influencing their nations' internal affairs. As much as I consider the Baltic citizenship policies during the new independence to be unfair, discriminatory and bordering on criminal, it is difficult to see how, with that past since 1940, these nations could have after 1990 become shiny, happy and harmonious multi-ethnic nations virtually overnight.
* Note that even the post-1990 citizenship laws are not based on ethnicity, as such, but jus sanguinis, having family roots in the countries in question. In Estonia, an ethnic Russian person who could prove that his/her direct ancestors lived in the country before 1940, during the first independence, would have received an automatic citizenship as much as an ethnic Estonian did. It was only those people that had arrived to the SSR during the Soviet era, or their offspring that were subject to the more difficult requirements - again irrespective of ethnicity.