Please try to login in incognito mode. Probably this is a browser cache issue. 

please watch the video i prepared now.

Firstly; I'm testing after logging in as admin, nofollow is still available.

then i test with a member login in a different browser, nofollow is still active.

then i test after member logged out, nofollow is disabled.

https://www.youtube.com/watch?v=GdlRupu9fSU

Please see how it looks when we're checking: https://www.screencast.com/t/KKl9reKC9

After logging in, it can be seen on pages with problems.

We don't see the plugin active on your website. Is it still active? 

I haven't removed the code yet.

I did wpdiscuz cache clearing again.
I followed the instructions found on the serpbabel site.
but the problem still persists.
Where else should I look for this problem? do you have a suggestion?

Yes, you can remove the code. However if somehow you see the attribute, please add it back. 

Thank you for your support.

I added the code you sent earlier to the functions.php field.

should i remove this?

The nofollow attribute in the please you're mentioning doesn't come from the wpDiscuz plugin. 

wpDiscuz adds the nofollow attribute in the two places I've mentioned here: https://wpdiscuz.com/community/postid/19090/ And the hook-code provided by us removes them. 

Probably the attribute is being added by another plugin.

Anyway you can use the solution provided here: https://www.serpbabel.com/how-to-fix-internal-nofollow-links-in-wordpress-for-beginners-with-pictures/

It should remove the attribute.