This is one of the most common questions from anyone new to travel rewards, and it deserves a straight answer instead of a sales pitch: it depends entirely on how you use the card, not on the fact that it is a rewards card.
Opening a new credit card does typically cause a small, temporary dip in your credit score, usually from the hard inquiry the application generates, and sometimes from a slight drop in your average account age. For most people with otherwise healthy credit habits, that dip is minor and tends to recover within a few months. It is a real effect, not something to dismiss, but it is also not the same thing as "rewards cards hurt your credit," which is a much bigger and less accurate claim.
The habits that actually determine whether a rewards card helps or hurts you are the same habits that determine whether any credit card helps or hurts you. Paying your full statement balance every single month, not just the minimum, means you are never paying interest and never carrying revolving debt. Keeping your overall credit utilization low, generally meaning you are using a small fraction of your total available credit across all your cards, protects your score. Neither of those things has anything to do with whether the card also happens to earn travel points. A rewards card used this way behaves exactly like a responsible, no-frills card used this way.
Where it genuinely can go wrong is if someone opens a rewards card and lets the promise of points change their spending behavior, buying things they would not have otherwise bought, or carrying a balance because the points feel worth it. Under those conditions they usually are not, since interest charges outpace almost any points value, and a damaged credit profile costs far more than a free flight is worth.
So the honest answer is this: a travel rewards card, used the same responsible way you would use any card, paid in full, kept to spending you already planned to do, is not inherently riskier to your credit than a plain no-rewards card. What actually determines the outcome is less about the card and more about the habits behind how you use it.