As always, it depends.
However, it is by no means certain that any public facing hobby project, such as a web app, is exempt from having to comply with the GDPR.
Since the GDPR is only a few days old, we have of course no case law based upon the GDPR itself yet.
However, when considering this, one should take the following two facts into consideration.
1. The "personal use exeption" in the GDPR is not new.
The personal use exemption is unchanged from the article 3(2) of Directive 95/46/EC. (There as a lot of lobbying for removing "purely" from the sentence – but drafters wanted to keep it.)
2. Case-law under the previous regulation restricts the scope of the exception
The ECJ has ruled on the scope of the personal use exception in two cases:
In both these cases, the ECJ took an extremely restrictive view, and concluded that the personal use exemption did not apply to the processing done by these individuals. In C-101/01 it can be argued that the hobby project as a blogger was connected to the controllers professional activity (she was a catechist in a local church, and blogged about her work. including her colleagues). But in C-212/13, there no such connection to professional or commercial activity. Here, the controller operated a CCTV to protect his home, but set it up to also capture public space, and that was enough for the ECJ to decide that the personal use exception did not apply.
Case-law based upon Directive 95/46/EC is in no way binding for a future court that need to rule based upon the GDPR. We need to wait for case-law decided under the GDPR to be able to have some degree of certainty about the scope of the "private use exception" under GDPR.
However, given what we know about how the ECJ has ruled in these cases in the past, I think it is hazardous to think that just because what you are doing on the web is just a "hobby project" not connected to professional or commercial activity, you are exempt from complying with the GDPR.
IMHO, you may be exempt, or you may not be exempt. I think it really depends on your activity in your hobby project, and to what extent this project processes the personal data of other people than yourself.