It's an ethnic slur all right. The significance of ethnic slurs depends very much on a range of factors. Where an ethnic group is subject to discrimination and persecution, these are clearly particularly significant. Where an ethnic group is seen positively and not liable to persecution they matter much less, if indeed at all.

And these things vary over time and place.

I've never heard any suggestion that Welsh people are particularly liable to welsh on a debt - it's not part of the kind of stereotype that even people who might be prejudiced against Welshness are liable to hold.

I think it would be possible to accuse someone of welshing on a promise in general, as an extension of the particular kind of promise involved with a bet.