Networking Question

Hey guys! I am a rising sophomore in an off-campus frat. I know joining a frat that got booted off campus (pledge hazing; the university has been trying to crack down on Greek life) isn't the best look for professional applications. Still, I joined them because I genuinely get along very well with all the guys, and none of the on-campus ones even came close to the vibes I was getting from rushing the off-campus one. This is a major national frat, so there are plenty of people in IB but from different chapters. Although I could contain my IB networking within my chapter, I don't want to stop contacting a potential connection. Would you find it a red flag if someone from the same frat as you but in a different off-campus chapter contacted you for networking? I don't plan on listing my frat on my resume for obvious reasons, but I want to use the name-brand of the frat as a semi-cold approach.