SMS Sieve

This is a simple, opensource SMS filter (see the source at https://github.com/prrt714/SMS-Sieve).

This app blocks SMS according to your rules. After you install it,
there is no rules, so you should create them first. This app can serve as either whitelist or blacklist. For example
you can add regular expression ".*" (less quotes) to blacklist
anything. Then you can add exceptions. If you add exception "+[0-9]+"
(less quotes), it will not block SMS from addresses containing digits
following the plus sign (e.g. +1234567). Blocked SMS are swallowed by
the app and logged, so you still can read it.

It need not any additional services to run in backround.It just
registers itself as SMS receiver, so Android knows what app should be
first to receive SMS.