McArthur, who had collected seven booking already this seasaon, was fortunate to escape with just a yellow card for a stamping incident midway through the second half.
But with three minutes to go he was dismissed for a second bookable offence.
The former Albion player is rated a talented performer, but there is concern about his lack of discipline.
Hastings boss Dean White didn't comment on the sending off but was pleased with his side's overall display.
He said: "I was very happy with the point but on the run of play we could have even got all three."
Fired
In a game which the visitors controlled for long periods, there were few clearcut chances, although Town goalkeeper Tony Kessell brought off two fine saves to ensure the point.
The first opening was created by Wisbech on 31 minutes when David Gibb fired straight at Kessell.
Two minutes later the home goal had a lucky escape when shots from Paul Jones and Terry White were blocked in quick succession.
Early in the second half a shot from Duncan Jones was well held by home goalkeeper Duncan Roberts.
Kessell then made a magnificent save to deny Anzy Furnival and minutes later Roberts did well to block a McArthur effort at the foot of the post.
Converted for the new archive on 30 June 2000. Some images and formatting may have been lost in the conversion.
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