It is unfortunate that the station time becomes a problem for some. Especially when NTP is not part of the station design. I say unfortunate but there is a solution. There are two ways to send data with the WU upload protocol. The station can upload data with a time stamp or it can just say time=now which then would present no problem for the ingesting server. If the station without NTP used time=now then there wouldn't be a need for time keeping on the station...and if the clock is off so what. Well I say so what as far as real data is concerned on WU but then would would happen is that data would be different at the station console than what is realized online if the clock is far enough off. Especially noticeable would be things like total daily rain if it is raining during the date change and other metrics like temp high/low could also be affected. But there likely is little recourse for the station owner to change the time stamp over to time=now as these things are hard coded in firmware. But you could write to your station manufacture and ask them to update the firmware so that the WU upload does change to use time=now instead of a hard time stamp.
The actual variable in the upload protocol though is not time= it is dateutc=. So it would need to be changed to dateutc=now for the data upload packet.
Some station owners though might be able to modify the WU upload. Some might be able to turn off a dedicated preconfigured WU upload and then instead configure a custom formatted HTTP upload. If your station allows it then you may want to consider looking at the WU upload protocol to manually configure the upload. Here is the relevant information to do that:
https://support.weather.com/s/article/PWS-Upload-Protocol?language=en_USAnother option if you can't change the upload protocol is to augment your station to use some 3rd party software and then you upload to WU via that 3rd party software instead. Many stations can be made to be compatible with software like Cumulus MX, Meteobridge, Weather-Display and WeeWX and you can then gain much more control over your weather upload. I would say don't get into all that just for the sake of WU...but rather because using such software will also increase the potential of your station do send data to more places than just WU. If you use such a system then your station that doesn't have NTP capabilities to synchronize the clock then does gain it via the system running this software. Because then your local software and its data will have proper time keeping. Then your display console becomes less relevant. Realize that by using this 3rd party software to solve the dateutc=now problem you've come full circle and also solved the NTP problem so then your station can use a proper dateutc= date/time stamp, so there would then be no need for dateutc=now.
TL;DRAdd 3rd party software to your station so that you can solve the time stamp problem if your station doesn't have NTP time sync capabilities.