The register page uses a BP template:
/registration/register.php
You could add some verbiage before the registration form in that template, perhaps a link to your blog post?
If you’re currently using the bp-default theme, create a child theme, copy /registration/register.php to your child theme and modify the template anyway you like (just don’t break anything 
Thanks for your answer, I’ll try this right away.
Hello @r-a-y
I’ve done like you said. Now I have child theme for default buddypress theme and I’ve added some text to the register.php page that says that users don’t need to register them selfs on the page to read our posts.
But I’ve realized that is only temporary solution. I still need permanent trick that will fix this automatic redirection for new users to the register page.
My question is: where we can find code that answers to that redirect and change it? I’ve searching it for a while without any success. Please help.
If your site has open registration like you say, then users shouldn’t be redirected to the register page when they’re trying to read a post.
Do you have any redirection or private BuddyPress plugins installed?
Users are redirected to the /register when they enter for the first time to the main site but from there its possible to navigate all the site content. I have tried to deactivate all plugins but that don’t helped a lot.
In other hand when we type in browser link to post it works without any problems. So its like that:
When new non-loged user types in his browser my site address hxxp://wwww.eziny.net he is redirected to wp-signup.php?new=mysite and from there to the hxxp://www.mysite.com/register/
Do you know how to change that @r-a-y ? Its very irritating.
I don’t understand your issue; I navigate straight to this URL:
http://www.eziny.net/
I am able to access your posts without being redirected to the register page.
@r-a-y you are able to access posts but when you entered to the hxxp://www.eziny.net/ you was not redirected to the /register ?
its strange, when I navigate to the site form link it work’s. but when I clear browser cache and type address mysite.com in browser its redirects me to the /register. Im sure its something wrong with it – ive tried different browsers and computers.
Like I said, if you’re using any caching or redirecting plugins please disable them and test.
After checking everything again I’ve discovered that I did not put the NOBLOGREDIRECT option in config.
Thanks for your time @r-a-y. You helped me a lot .
