State verbs as you correctly say are not usually used in the progressive. It is possible however to do so in some cases. This, however, can change the meaning. The English language is constantly developing and evolving and previous unaccepted usage of the language has become 'accepted'. McDonalds are almost solely responsible for the stae verb 'love' being used in the progressive. Because of their global audience and influence it has now annoyingly found its way into everyday usage, eg, I'm loving this hamburger!!
'Have' when it implies possesion is used as a state verb,eg, I have a blue pen. But when 'have' is used for activities it can be used like an ordinary verb, eg, I'm having a shower, I'm having breakfast. Similarly, the verb 'think' is a state verb when used as opinion, eg, I think you're right, but when used as a mental activity it can be used in the progressive,eg, I'm thinking about my family.
Another example would be the verb 'see', normally used in the simple form,eg, I see a man outside in the street. 'I'm seeing my friends later' is correct usage but alters the meaning, and now means 'I am meeting my friends later'.
Anyway, misuse of state verbs is a as ordinary verbs is a source of great annoyance for me. McDonalds are now responsible for both bad food and bad English!! As a teacher of English as a foreign language I wish they would restrict themselves to influencing my students' diets but not their use of good English.
PH