Is it bad to open new credit cards?

While it’s true that a hard pull can hurt your score a little bit, they’re not that big of a deal. Hard pulls and new lines of credit only account for a small percentage of your score, and they’re very low impact. Plus, hard pulls are typically scrubbed from your credit report after about 2 years.
As a general rule of thumb, you shouldn’t let hard inquiries on your credit keep you from applying for credit cards, other loans, or even apartments. I can’t recommend that you go crazy with applications, but a few hard pulls over the course of a few months or a year aren’t going to be the end of the world. The impact on your credit score is minimal, and it’s much better to focus on making on-time payments and keeping utilization low than it is to focus on hard pulls.