I don't know if what we do would or would not apply to you, it could in time.
We are the same anti-aggression/violence and it does reflect in what we like so we really don't have the exact issue you do- ex. my DH hates American Football- it goes against what we believe so it's not on TV nor would be go to see it.
We are also very anti-competition (organized team sports) and greatly favor non-organized, non-competitive sports and solo sports.
My DH made up his mind prior to our DS birth (years!! prior) that there would be no organized team sports and his adamants has only grown since we had our DS (soon to be 5). We have seen families that are not like us and frankly we don't like how the kids turn out.
In our state (PA) with Penn State stuff this has really hit home to many and I know some have drastically changed their prospective and this is applies to allowing participation for their children- to many it was a wake up call on many fronts (team favoritism/worship, participation, etc and YES for some a deep reflection into the the whole aggression as well) but there are some it didn't do a thing to. Personally we know one die-heart that no longer is and she did a drastic turn around regarding her DS playing based on the violence involved.
I do feel that you are sending a mixed message if you watch such sports as American football (and numerous others) and you don't push, shove, hit, punch, etc., your child. How some can explain it away I will never know- I (we) don't like it so it's easy for us to explain what turns us off about it and how we view it as wrong on many levels.
Sorry I really can't advise you as you are look for- to me it's all the way or you are really not committed if you make exceptions and those exceptions are for non-important meaning-IMO-a sporting competition (EX. not fighting someone off that is attacking you in a dark alley)....at that.
Unless your definition (aggression, violence, etc) is not what the words really mean I don't know how to justify it but that is me.
Some people do change and as their children age, they realize hey I don't want the air kicked out of my kid and putting him in a helmet to run at another kid is just not normal.
All the so called values that many claim come from "sports" can also come in other forms and without beating each other up to learn them.