Dear zstadler,

thank you for your message. Actually, I didn't mind if you removed the tag, however…

However other routing engines, e.g. Graphhopper treats tags in a completely different way: https://graphhopper.com/maps/?point=32.845701%2C35.51034&point=32.849325%2C35.508516&profile=foot&layer=OpenStreetMap

Indeed, OSRM itself seems to treat them well:
https://www.openstreetmap.org/directions?engine=fossgis_osrm_foot&route=32.846252%2C35.50998%3B32.849452%2C35.508542#map=18/32.847857/35.509266

So if we would change tag that would be actually a "tagging for the renderer" action that is strongly discouraged by the community:
https://wiki.openstreetmap.org/wiki/Tagging_for_the_renderer

So I would rather suggest to contact the developers of OSRM and discuss with them the issue.

Cheers,

Gábor