What are the minimum conditions by which one is considered a Muslim from the viewpoint of Wahhabism?
There is no one better equipped to answer this question more than Muhammad ibn 'Abdel-Wahhab, the one Wahhabism is named after. From his book The Three Fundamental Principles (Arabic: الأصول الثلاثة), when discussing the second fundamental principle, he says:
الأصل الثاني: معرفة دين الإسلام بالأدلة
وهو الاستسلام لله بالتوحيد، والانقياد له بالطاعة، والبراءة من الشرك وأهله
وهو ثلاث مراتب: الإسلام والإيمان والإحسان. وكل مرتبة لها أركان. فأركان الإسلام خمسة: شهادة أن لا إله إلا الله، وأن محمدا رسول الله، وإقام الصلاة، وإيتاء الزكاة، وصوم رمضان، وحج بيت الله الحرام
The second fundamental: Knowing the religion of Islam through evidence
It is the submission to Allah alone, and yielding to Him by obeying His commandments; and absolving oneself from shirk and its people.
This knowledge has three ranks:
- Islam (submission)
- Eman (faith)
- Ehsan (perfection of worship)
Every rank has its own pillars. For Islam, there are five pillars:
- Testifying that there is no God but Allah, and that Muhammad is His Messenger.
- Performing prayers
- Paying the Zakat
- Fasting the month of Ramadan.
- Pilgrimage to the Sacred House (Mecca).
So the definition of a Muslim according to Muhammad ibn 'Abdel-Wahhab is one who upholds the five pillars of Islam.
This question is hard to answer. Because to answer this question one must really first define wahhabism. Also, is wahhabism just a name for salafism? It seems the tag salafi is used in the question, so maybe you are asking for that. Because there are opinions that salafism is wahhabism, just with different names.
If we say they are the same, for the sake of simplifying this answer, would that even mean that all salafi scholars follow the same opinion of who might be called a muslim?
Most salafi scholars says that whoever abandons the prayer is a kafir1. While there are some who actually follow the opinion that you aren't a kafir, even though you don't pray.[I will need to back this up later] This could get deeper and deeper, it's a broad question.
The conclusion here is that, even the salafi/wahhabi scholars will have different of opinions of who is called a Muslim. But generally they would call anyone a Muslim who claims to be a Muslim, if otherwise isn't proved (for instance, not praying of laziness and other things like this).
Then if we count other groups like ISIS, which calls themselves salafis, the answer could differ here too.
When I speak about salafi scholars, I intend nowday scholars, not counted to be among the salaf.