[susan53]

Two reasons - grammar and meaning.

Grammar

1. To contact someone (verb - contact + object) Eg: I didn't feel well so I contacted my doctor.

2. To have contact with someone ( verb have + object contact (=noun) + prepositional phrase). EG. I haven't had any contact with John since our argument in 2005.


Meaning

1. To contact someone usually means to get in touch with them by phone, email, letter etc.

2. To have contact with someone can mean this but also means to meet them physically.

So which construction you choose will depend on the type of contact involved. I suspect that your sentence refers to all types - distanced contact and physical meetings (or possibly just physical meetings), so you'd probably need to say :
The manager should feel you will be ... friendly to people you will have contact with.