Trustable or trustworthy?

While it is true that trustable does appear in many dictionaries (and therefore may be safely considered a "real" word; whatever that means), trustworthy is the more common choice by far.

Trustable has recently seen an increase in use, but it is clearly nothing close to the use of trustworthy. Trustworthy is certainly the more common option.

In terms of meaning, there does not appear to be any substantial difference.

Since there is no possibility of someone being trustworthy but NOT trustable or vice versa, it would seem that the words are synonymous

If somebody or something ​is worthy of trust, then you may / will be able to trust them. The distinction suggested above for senator Whiplash is meaningless because trustworthy does not mean it/he,she,they is/are unconditionally 100% trustworthy ad infinitum for everything, unless explicitly stated. Neither is trustable elsewhere defined as only being used when someone/something has a defined limit of trustworthiness. A logical reason for the new word trustable to evolve could be that people do not use worthy in as widely as they would have say 100 years ago. Today you would mostly describe a person or product as trusted, reserving worthy for distinctions carrying honour (medal, knighthood, prize). When worthy is used as it were 100 years ago outside of that context it appears stuffy or pretentious today, (the worthy dog vs a trusted companion, worthy choice vs good/excellent choice).

While often used as synonyms, it seems to me they are somewhat different. Trustable implies able to be trusted, and trustworthy implies worthy of trust. Being trustable doesn't necessarily imply trustworthy, and vice versa. The adjective you use should depend on what concept you are using.