I would hazard a guess that this won't move the needle that much, as recent shifts tend to be driven by personal economic prospects rather than social political prospects. Traditionally Blue states of late have seen population drops while red states have seen gains with the most common factors being a high tax state to low tax migration. Texas and Florida seem to be the biggest gainers with zero income tax (and pretty decent weather). But Colorado (Blue but low tax) also seems to be making gains. Likely we won't know for about decade as the next census will be held in 2030 and the results will not be readily known until 2031.
Edit: It certainly doesn't look like socital issues are the core concern of Americans in this recent AP poll. According to respondents, Inflation (40%) and Gas Prices (33%) are their number one concern. Gun Issues are at (30%) (Note, the phrasing does not indicate if respondents are pro or con on Gun Control), but then comes Immigration, Economy (general), Education, Environment, all before Abortion (16%) is ranked first by respondents.
In the political break down, among the top five concerns, Economic (Inflation and Gas Prices) issues take first and second priority of the top five spots of Republicans and Independents, with both sharing Gun Issues as the 5th priority. The only difference is Republicans are more concerned about Immigration (3rd) than the General Economy (4th), while Independents reverse these concerns ranks for these two fields respectively.
Among Democrats, the break down is Gun Issues (1), Inflation (2), Environment (3), Education (4), and Abortion (5th).
From this it tends to show that there might be motivated self-interest to move based on gun laws between states, but money is more consistent motivator for all three major groups.