Disabling manage_woocommerce disables access to Dashboard

I am having the same problem

Add manually the ‘view_admin_dashboard’ capability and grant it to a selected role.

I tried that already. Didn’t work.

It’s possible that some other plugin is involved. Try temporally deactivate all plugin except WooCommerce and re-test user access. If that will help, activate plugins back one by one to isolate a reason.

Also look at the “WooCommerce admin bar access” part of this article.
Using custom filter or granting ‘edit_posts’ to a role may help too.