Is it rude to look for jobs while being employed?

I'm trying to look for other part time jobs, while currently in one, but i'm not sure if that is acceptable or not.

Both jobs that I am currently on and the job i'm interested in are in retail, but different department/sectors (if that makes sense). They are not in competition with each other.

I have been with my current job on and off since March because of Lockdown and I feel like this new role would suit me better. I'm not sure if different cultures would apply differently, but I'm from the UK if that helps.

It's a better pay, and it's not like I'm for sure getting that new role. I just somehow feel guilty looking for other jobs.

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