Well, know your customer and your country if you know lots of people using bitcoin on your country, then why not give it a try, bit of course, don't just bitcoin for payment, give your customers options for payment.
Of course the main payment system will still be with fiat, eventually, bitcoin and cryptos would be an alternative option.
The store is more focused on local sales in the UK for now... as far as I know, cryptos are quite popular here.
I like the idea of being able to get some cryptos (not everything) instead of fiat as payment... it would save me some time instead of having to buy from the exchanges

The one of my main concerns is: how safe is it to accept cryptos as payment on a website?

Yes, it is safe as bitcoin payment is irreversible, besides the volatility and confirmation time, nothing to worry about it.
Since many people using bitcoin in the UK, then it's a good idea to add a crypto payment option.
Buyer and seller should understand that both parties have to wait until 1 confirmation received on your wallet, then you proceed buyer's order.
OP's concern is more like on implementing of the payment gateways on a website which is more technical and need a developer to make it work.