I ran into this situation this morning. I was attacking with Willas Tyrell against Martell and The Red Viper was in play (Immune to character abilities). Neither myself nor my opponent were sure whether Willas's ability of not counting opposing characters STR applied in this case. Can anyone illuminate me on this? Thank you!

Just because Willas' ability isn't a triggered effect does not mean that it is not a character ability.  It is an ability and it is on a character.  Furthermore it is trying to directly effect TRV (unlike Pyatt who is changing game mechanics), so I would say that TRV is immune to it's effects. 

Going to search a little to see if I can support this though…

Researched:

(3.7) Card Abilities

"Card abilities" (i.e. "Character ability," "Location ability," or "Attachment ability") refers to anything in a card's text box, except for traits, keywords, and flavor text. "Card abilities" also refers to any abilities (again, keywords and traits are excluded) gained by card effects

(3.14) Effects of Immunity  

The effects of a character ability cannot be applied to a card that is immune to character abilities.

 I'm pretty sure the Red Viper prevails over Willas in this instance (how thematically appropriate!).

Thanks you for the responses and the time expended to search and support them. Thematically appropriate indeed!!!