Research jobs in psychology do exist - I think most of them will be following an academic career pathway (ie get a PhD then stay in academia). Research is competitive - if you study a degree you don’t like as much and aren’t as good at for career purposes and then don’t do very well in it because of that it’s probably not going to be super beneficial to your career. Also doing research as a job (I’m a Psychology PhD student, so this goes for academia at least) can be very time consuming, you really have to love what you’re doing or you will probably just have a horrible time. Doing a psychology degree wouldn’t cut you off from neuroscience in the future - a psychology undergrad could be a way into a neuroscience PhD depending on your research experience and the modules you took.
Basically I would suggest doing what you’re passionate about and making an effort during undergrad to make connections and get research experience wherever possible so you can competitively apply for research assistant jobs/PhDs when you graduate which is the first step.