Hi arjan.janissen and Seemon, I'm sorry that the issue is persisting for you. As mchain says, the only permanent resolution to this is for the WhatsApp devs to change how they detect the browser. For the workaround, rebooting should not be necessary, but the Anti-Fingerprinting component must be turned on (the other toggle-able Security Center settings are unlikely to affect the issue).
Some users have reported that the workaround wasn't effective until they had used the Privacy Cleaner (accessible from the Security Center) to clear "Cookies and other site data", "Cached images and files" and "Passwords and other sign-in data". I would advise to close the WhatsApp website, use the Privacy Cleaner to clear this data (Open Privacy Cleaner from the Security Center, click the "Advanced" tab, select the Time range for "All Time", select the listed items and click "Clear Data"), and then attempt to open the WhatsApp website again.
Please let me know if you still experience any further issues with the website.