Support

I have read other posts and I saw I can rule out Admin Tools if I disable it and see if the problem is still there.

You are missing just one thing. You also need to replace the contents of the .htaccess file in your site's root with those from Joomla's htaccess.txt (if you don't have a copy of htaccess.txt, here it is: https://github.com/joomla/joomla-cms/blob/staging/htaccess.txt).

If this addresses your problem you need to follow the instructions in https://www.akeeba.com/documentation/admin-tools/server-protection.html#determine-required-exceptions to determine any required exceptions to the site protection feature of the .htaccess Maker.

I am going to use membership pro on my site for paid subscriptions. Is there anything I should do to prevent users from subscribing or will that work without any changes?

We haven't heard of any incompatibility with Membership Pro. Caveat: what is most likely to cause a problem is not the component itself but any third party payment plugins. We've seen that some very few payment plugins for other e-commerce extensions had .php files they expected to be directly accessible over the web. In some cases that's inevitable (having done payments integration work I can attest to that). If you have a third party plugin which requires something like that you'll need to add an exception for that file in the .htaccess Maker.