RyanAir are proud of spending as little as possible looking after their customers. You can try asking for a refund by another means, but your chances are poor. I'd count yourself lucky you've been able to get a cash refund at all.

You could also ask Revolut why they won't let you pay cheques in, but your chance of success is also poor there.

Instead get a standard bank account, which UK institutions expect you to have. For example, a Halifax Current Account which can be opened online and like most UK bank accounts has no charge. Once the account is open, you can pay in the cheque by taking a photo with your phone. You will not need to pay a fee, and you will not need to leave your home.

Legally, you can refuse

According to the Cheque and Credit Clearing Company:

Cheques are not legal tender and never have been. Even today, if you owe someone money they are not obliged to accept a cheque. A creditor is entitled to be paid in legal tender and can refuse payment in any other form.

So legally, you are not obligated to accept the cheque, and you can ask Ryanair to pay you in another form. The only forms of payment that you can't refuse are those that constitute legal tender.

What’s classed as legal tender varies throughout the UK. In England and Wales, it’s Royal Mint coins and Bank of England notes. In Scotland and Northern Ireland it’s only Royal Mint coins and not banknotes.

There are also some restrictions when using small coins. For example, 1p and 2p coins only count as legal tender for any amount up to 20p.

So, you can certainly ask Ryanair to credit your Revolut account instead. But...

Practically, you should accept it

As others have said, in answers and comments, you are likely going to be better off to count your blessings, accept the cheque, and figure out a way to cash or deposit it. The answer from thelem has some suggestions, and there are other posts on this site that discuss ways to open a simple bank account. Even though modern society is moving away from a number of traditional banking concepts, there are still times, as you are finding, that having a bank account is a good idea. I recommend you get one, for this and possible future needs.

Caveat

As Steve Melnikoff points out in a comment:

Legal tender only applies when a debt is owed. It is possible (if unlikely) in this case that Ryanair don't actually owe OP the money, but have chosen to issue compensation as a matter of policy or goodwill. It's a technicality, to be sure, but I'm not sure it's worth pursuing.