People are not receiving my text messages?

I have an Iphone 5c with AT&T. I'm sending text messages to people who do not have me in their contact list (for my friend who doesn't have access to a cell phone at the moment). When I send messages to these people, they do not reply or see my messages. For the iphone users I'm sending messages to it doesn't say 'delivered'.
When I send texts to people who are in my contact list, and I'm in theirs, they receive my messages.

Do I have to be in someone's contact list in order for them to see my text message?

You NEED A COMP TECH

IMessage does weird thing when sending texts to non-iPhone users sometimes.

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