This shouldn't be an issue. I'm a dual citizen and have the enter the US on my US passport, but generally enter other countries on my other passport (Canada) unless there's weird political stuff or one visa is easier to get (when the US is not visa-free, the Visas are always super expensive). I tend to book flights under my US passport, but have my Canadian details entered at check-in either via app or at the counter.
It is absolutely no problem and literally no one will care.