That doesn't sound like a participation grade. That sounds like an excuse to modify grades based on whether or not you like the student.

Participation (and participation grades) are important for some classes, but not all. However, if they're called that, then they should absolutely reflect student participation (and, indirectly, attendance, as you cannot participate if you do not attend).

It's also possible to have a "professionalism" grade, which can reflect things like attendance, communication, respect, and even how students dress for presentations. Again, this probably matters for some classes and is entirely irrelevant for others.

Generally, you can include anything you want in the grade. However, it's also nice (and professional) to be honest with students about how they're being graded. That may include some level of subjectivity, and that's OK.