I’m going to start with this point first because it’s the problem with the whole line of thinking. Democrats use the notion of “dog whistling” to brand Republican policies racist based on the premise that republicans are racist. But their support for that latter assertion is that republicans support supposedly racist policies. The reasoning is completely circular (and unfalsifiable).
Republicans opposed the creation of the welfare state in the 1930s when pro-segregation democrats introduced welfare programs. They likewise opposed the expansion of federal government at the expense of the states by vicious racists like Woodrow Wilson. So what are we to infer from Republicans’ continued support of the same policies before and after democrats abandoned their support for segregation?
To circle back to your first point, why would LBJ fear losing the south? Why would southern racist democrats switch to the party that had supported the civil rights act even more strongly? That’s like Muslims switching to the GOP because they’re mad at Biden for his support of Israel.