Let me get this right. Some person working in the media office in Merseyside HQ has sent a twitter DM to say that they will look into the matter as a hate incident.
Well good luck explaining that one to your police colleagues, mate. 
Yes, I think this is an important point, much as it was said in fun - having witnessed first-hand a group of Merseyside officers dealing with a DV incident this weekend, I can't imagine these particular officers dealing with willy stickers in anything but a calm, professional manner and then having bloody good laugh back at the station.
It is not the coppers on the ground who operate the force's Twitter account, and "we are investigating" is, tbh, a set of weasel words that tell you nothing about the scope of an investigation.