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If I want a Credit Card offered through a different Credit Union should I slowly transition my banking to that CU?
No. There's no inherent reason to link the place that you bank with any other financial service. There may occasionally be benefits; for instance you can sometime get lower rates on mortgages or loans by having a a checking account with an institution. Or perhaps it'll be easier for you to make a same-day payment on a credit account. There could be some negatives as well. If you fall behind on a loan account, the bank may take money from your savings/checking account to satisfy your debt. Choose a bank or CU that's convenient to you. Choose a credit card from whatever bank or CU provides you with the best benefits. If that credit card is coming from a CU that requires a savings account for membership, open a minimum balance savings account and apply for the product you're interested in. If your credit is as good as you claim, they'll be happy to offer you the credit card regardless of whether you do your day-to-day banking with them.