As has been stated, you don't need to actively bank with a credit union to apply for one of their credit cards. That said, one benefit to having account activity, and significant capital with a CU, is to increase the likelihood of having a larger credit line granted to you, when you do apply. If you are going to use the card sparingly however, then this is a non issue.
That said, if you really want to maximize card benefits, then you want to look for cards with large sign up bonuses (e.g. Chase Sapphire, or Ink Bold if you have a business) and sign up exclusively for those bonuses. These cards offer rewards in excessive value of $1000 in travel services (hotels/plane tickets), or $500 cash back if you prefer straight cash back redemptions. If you prefer to keep it really simple, you can sign up for a cash back card, like the Amex Fidelity, which offers 2% cash back everywhere, with no annual fee (albeit the cash back is through their investment account, which you don't actually have to 'invest' with).
Personally, I have the Penfed card, and use it exclusively for gas (5% cash back). I also have a Charles Schwab bank account, which I keep funded exclusively for ATM withdrawals (free ATM usage, worldwide, 100% fee reimbursement). I use the accounts exclusively for the benefit they provide me, and no more and have never had an issue. I also have 3 dozen other credit cards which I signed up for exclusively for the sign up bonus, but that's outside the scope of this question. I only mention it because you seem to believe it is difficult to get approved for a new credit line. If your credit is good however, you won't have a problem.
For a small idea, of how to maximize credit card bonus categories, I would advise you read this. As mentioned in the article, its possible to get rewards almost everywhere you shop. In short, anytime you use cash, you are missing out on a multitude of benefits a credit card offers you (e.g. see the benefits of a visa signature card) in addition to points/cash back.