Is sports arbitrage betting legal?

Yes, sports arbitrage betting is 100% legal.

All that you are doing when you engage in sports arbitrage trading is placing a series of bets on opposing outcomes of a sporting event, which happens to guarantee a profit. Therefore there is nothing remotely illegal in arb betting.

Arbitrage is also popular in other contexts such as stock markets and Forex (foreign exchange / currency markets) where price differences can be exploited to guarantee profitable trades.