The demonstrated cross wind limit of the 737 is 35kts.
This is normally, if not universally, an operational limit.
We have limits on when doors can be opened and limits on when we can taxi.
I have landed in winds gusting 60+ kts and its not fun.
On this particular day the wind readout at 500' RA (radio altitude) was 88 kts.
The decision about whether to land will ultimately rest with the Commander.