It’s not so much that “it” doesn’t support “it”, whatever “it” may be. It’s that you’re not supposed to have the RewriteEngine On directive twice in the same .htaccess file because that’s not how .htaccess files work.
Things can get confusing fast if you just paste in different .htaccess snippets from different sources without fully understanding how they work, and accidentally may end up causing conflicts between the different snippets, with unexpected consequences as a result.
The mod_rewrite module is enabled on our hosting and all mod_rewrite directives should just work. And so far you’ve old said “it works on my machine”, but that’s not exactly strong evidence that the issue must be related to .htaccess rules.
Can you please be a lot more specific? Can you please clearly state which URL/page is not working, what you expected to see, and what you actually see here?
When I check your website’s main page, I get redirected to /giris.jsp. Despite the URL, you have .htaccess rules to reroute it to /giris.php, so that code is executed. But that page itself does not return any content, and the Network tab in my browser tells me that it has a response code 500.
So I think your .htaccess code is not the problem here. Instead, your PHP code is crashing.
There are all sorts of reasons why PHP code could crash here but work on your local machine, ranging from upload issues, configuration issues or compatibility issues. In most case, those can be solved, but you will have to do some troubleshooting yourself first to see why your code is crashing.