How do I copy and paste a text address in the messages app?
I think it's just the way you're pressing on it that's causing you the problem.

Assuming iOS has recognised it as an address (typically it would appear in blue and be underlined just like a traditional hyperlink), just tap on it gently for about a second or so and you should get a range of options. One of the options will be Copy. Select that and you can then paste the address as you want into another app etc.

If you just do a quick tap, then it'll take you to the Maps app as you describe.