modern gaelic(s) and possible cognates or loanwords (play)

[RobertColumbia]

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You are right. Celtic languages are unlikely to directly have caused the High German consonant shift, otherwise it would have been most pronounced in Alemannic dialects. My idea was more about monks coming from Ireland to Germany, having problems to pronounce some of the south-German sounds, and creating a compatible compromise, that is then promoted via (monastery) school teaching. Say - the locals pronounce "open" as "opfen", the Irish monks as "oscail" or "ouvert", and what emerges as compromise is "offen"....

In addition, if interference from Celtic languages had caused the High German consonant shift, you would expect that English would be the most effected by the shift due to the large-scale assimilation of Celtic speakers to English. In fact, what we find is that English is more or less the West Germanic language that has been least affected by consonant shifts. For example, English preserves the "th" where nearly every other Germanic language has migrated to "d". Compare English "thou" with German "Du", and compare English "through" with German "durch".