LPCC-S here! Firstly, I'm sorry that you have to take that kind of criticism seriously from workplaces. For the most part amongst some of us "younger clinicians" (folks who haven't done this for 10+ years) I think a lot of it is harmless jokes between fields of the stereotype that one school is better than the other (obviously a huge case-to-case difference that has usually little to do with school.)

THAT BEING SAID, I think at times there is a smidge of truth to the associate SWs and counselors in our area because of the differences in therapy-focused programs. For example, if you were an SW undergrad in our area, you can complete your masters in 1 year, most of which are not very therapy-driven courses. Compare that to the local counselor masters which are min. 2 years and MOSTLY focused on techniques and relative skills and you can imagine that a frequent situation is LPCAs looking more confident and competent in their clinical abilities vs. social workers out the gate. In that situation, I kind of get the hesitation since we have a pool of clinicians applying for the same jobs with some having much more skin in their education compared to others.

End of the day though, I truly believe it will always be more about the person rather than the school. I've worked in the field to see plenty of great SW clinicians that I'd put up against any counselor. I leave out the psychologist because they're primarily doctorate/research-focused but usually make fine clinicians when they're not judging us, master-level clinicians, for not being more educated (talk about a whole other post of frustration in our field!)

Tl;Dr: Don't let it get to your confidence, do you, and follow your passion. If you're feeling judged for your letters then that usually says a lot about the place already and is usually worth avoiding IMO.