Can university educators provide private tutoring to anyone seeking it?
Many university professors have side gigs doing consulting work for industry, writing, starting companies and doing many other things. At all universities I’m familiar with this is permitted and to some extent even encouraged. Usually there will be a policy in place specifying how much outside work is permitted. For example, here is a link to the relevant policy at the University of California system.

As for your specific question, tutoring students at other universities is not any different from any other kind of side work. As long as the professor is in compliance with their institutional conflict of commitment policy, this is totally fine. The only other case where it would be a problem is if they want to make money from tutoring students at their own institution.  This would create a fairly blatant conflict of interest and would likely be regarded as unethical. See for example this question.