I don't think it's so much that the long time residents did not have issues with parking, they always did. Ask any old fireman about trying to traverse through Southie in the winter and they will tell you the issues with parking during the winter always existed, they just get a lot more publicity these days.
However, as an insular neighborhood where literally everyone knew everyone, they were able to make it work. The gentrification of the neighborhood has eliminated that luxury. IMO, the anti-car sentiment is quite misguided as people must have the ability to commute to jobs no matter where they live, and public transit simply does not go everywhere the jobs are.
This isn't your parents life, where they worked for the same company for 40 years and were therefore able to settle close to their work. The reality is that you may sign a one year lease with every intent of using mass transit or biking to get to work, only to find yourself out of job a week later and then finding your next opportunity in the suburbs. That said, I would suspect that the locals would suggest that you never should have moved there in first place.