Bloodoathing (or changing alignment any other way barring immortal sponsership)
will make you into a Betrayer on the following conditions:

1) Any Class with an Alignment Change (Non-ethos change)

2) As a priest, you change ethos and/or alignment.

Doing either of the above two conditions makes you a Betrayer either
to your race, class, or religion. Being a Betrayer, no matter who you
are, has consequences that will pretty much screw your character, unless you
really want to be in for a tremendous roleplaying experience. Expect to be in
for a very tough life.

Some things you can expect to happen to you as a Betrayer:

Losing spells

Losing songs

Losing supplications

Losing specializations

Losing other key skills

Extreme vulnerability to certain types of attacks/spells

I'll say it one more time, just for anybody thinking it's cool to be a bloodoathed
Storm Warrior. Becoming a Betrayer will screw your character. 99% of
people do not have the Roleplaying ability or dedication to reacquire their
lost powers, and you will generally be hunted by everybody without regard to
your motivations. Do so at your own peril.