The website of the Wikimedia Hungary is currently using HTTP-protocol as default. It should use HTTPS, mostly because of its donation interface.
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we don't control the domain AFAIK nor the server where is hosted (193.218.98.220 / dyna-220.sx5.cable.tolna.net)
This is invalid then. You must contact your local administrator. Wikimedia Foundation cannot do anything but recommend fast switching :).
Correct, neither the domain itself (Registration, DNS) nor the hosting of any resources for it, belongs to the WMF. http://www.domain.hu/domain/domainsearch/ can give details to look up the owners.
If wanted, WMF can create a wiki hosted on WMF's infrastructure. If you should want WMF hosted wiki, please create a task via this manual https://meta.wikimedia.org/wiki/Setting_up_an_internal_Wikimedia_wiki. But if you would like to have the same content, cooperation from local system administrator will be required.
@Tgr already set up the https protocol for the website: https://wikimedia.hu/
We already had a discussion that this should be default for the website, but we postponed it because we wanted to be sure that no service will be broken. Tgr knows the technical details better than me.
I know that HTTPS is available, because I spotted a "use security connection" option on the login page. However, I am using HTTPS Everywhere but it doesn't recognise it; the only option is typing the htts:// URL.