I am currently managing an affiliate program for a company with various trademarks. We are considering restricting our affiliates from bidding on our trademarks and similar phrases. What do other managers and affiliates feel about this change in TOS?

I think managers need to protect their intellectual property and avoid affiliates outbidding them, esp. with the new Google rules.
Besides, if a person is searching for your trademark they are obviously looking for you based on your branding efforts and someone else should not get a commission just because they ranked higher. Affiliates should be used to refer new customers not already aware of your company and for more generic terms.

I think it is ok to not allow bidding on trademarks, but I think with Merchants restrict bidding on non-trademarks, that is going overboard.

I dont think a merchant can keep affiliates from bidding on "non-trademarks". They may ask them not to used certain words like cheap, fake, replica, etc. because it may do harm to their brands.