I can't find any indication that the sound recordists were on strike too, so I suppose the technology at the time just didn't enable very good audio on location, or at least on the locations they had available to pass as UNIT HQ.
The studio sound technicians may or may not have been on strike, but with no studio cameramen working they wouldn't have been of any use (film sound was done by different people, probably from a different union, so trying to use the studio sound people would likely have led to another demarcation strike).
Getting the extra resources to shoot the studio scenes on film was a touch and go job, so they'd have had to accept any film sound people they could get, experienced or not, and probably not for as long as they'd like to have had them.
Technology obviously wouldn't be an explanation for Spearhead having noticeably weaker location sound than other stories of the time. Lack of time would be.