makes me think you could avoid authentication by giving neither the username nor the password, but you might still get denied because if you were not denied, then anyone could send mail (e.g. spam) anywhere.
Open mail relay is the term for this, and it’s bad practice. Generally port 25 these days is primarily used for relaying between mail servers. 587 or 465 are for client submission, however I can’t make a connection to those from here, only to 25, so maybe they’re only accessible from an online.nl IP address, but would they want authentication as well? If they only accept mail from their network, but you’re not on it, are you stuck?
E-mail instellingen Online.nl says outbound e-mail uses smtp.online.nl port 587 (another sign 25 won’t do). When and if you can finally get connected, port 587 is usually starttls (switches to TLS), and 465 is smtps.
Cleartext Considered Obsolete: Use of Transport Layer Security (TLS) for Email Submission and Access
EDIT: Actually they might still have network restrictions on port 25 to keep it less than completely open, but it seems to go against usual practice and their documentation. The best plan might be to ask them to help.