Redirect taxonomy term page links to a View page's exposed filter
After some trial and error and guesswork I've got it working using Page Manger (part of the cTools module):


Under Structure > Pages, Enable and Edit the Taxonomy View page - if there isn't one, you  might need the Page Manager Existing Pages module
Create a "HTTP Response Code" variant
Select "301 Redirect"
For the default pattern, enter something like:


  pagename?%term:vocabulary:machine-name[]=%term:tid

Test this. There might be cases where the field name stub used in the exposed filter doesn't match the actual vocabulary machine-name and where editing this in Views isn't a good option. For example, I had one field named "colours" not matching its underlying vocabulary "colour". You might also have exposed filters using strings like field_fieldname_tid which you might have reasons to not change. If this happens:


Go back to "Summary" in Page Manager for this override
Click "Add new variant"
Give it a sensible admin title (e.g. the vocabulary name) else you'll hit an error later on as it'll match the default name
"HTTP response code" again, and tick "Selection rules"
Choose an appropriate selection rule (probably, "Taxonomy: Vocabulary", then tick the awkward vocabulary), continue
Choose 301 redirect again, and enter the same pattern as before but with the token %term:vocabulary:machine-name replaced with the string used by the exposed filter, for example pagename?colours[]=%term:tid