Posteo is great for business. It's a professional and competent company that respects your privacy to a good degree, and has a clue about security. In a sense it's MORE professional than trying to DIY, unless you really know what you're doing. I would feel encouraged to see a business use Posteo when I receive the email. It tells me that your business probably cares a little about security and/or privacy and possibly the environment too. Total kudos for using Posteo from me.

What I think is completely unprofessional is to use your ISP's address for business email. The number one unprofessional business move, in my opinion, is to have your business website on Facebook/Meta, Twitter or any other enshitified corporate social media site. You won't get my business. I'll go anywhere else no matter how inconvenient.

Anything beside the own domain is unprofessional, if you run a business.

As an individual i think it speaks for yourself as caring about the environment and privacy.

Try cock.li

As a personal email its just fine. I've had people comment on the fact that my "firstname.lastname@posteo.org" made me seem more professional than others using whatever @gmail.com address they could get their hands on.

People said Gmail was unprofessional in 2005, don't worry too much about what business majors think.

No, not at all.

That sounds like some often parroted but never actually a thing job hunting advice from the late 90's.