Hello,
Yes, happy that you see this point too, I try to reproduce your issue on my localhost and wasn't able to, so I start to analyse the Date Picker code and don't find where an element won't allow to select current day...
And so, I try to process some quick test on your website, and analyse your configuration, that's why I want to remove some configuration like "Hour for extra day" because I think that may be linked with your issue.
But that may be linked to time zone too, but can't be sure of it... Continue to process some tests, and please that it works or not, keep us informed, that's allow us to progress on this subject OR confirme that everything is good in our code.
Awaiting news from you.
Regards