It'll be interesting to see how this plays out, given the conflict here.
On the one hand, 'gender critical beliefs' are a protected characteristic, so if they were refused service on this basis, that is unlawful. Alison Bailey recently won a Sex Matters funded case against her vet practice for their refusal to continue to treat her dogs for the very same reason. Although the vet practice argued it was because of her behaviour towards staff, she still won. It is of course awful that certain classes of people can abuse the system in this way, but it's the law.
(For a belief to be considered a protected characteristic it must be cogent, serious, cohesive, and important, and it must be worthy of respect in a democratic society, not incompatible with human dignity, and not conflict with the fundamental rights of others.
Obviously, “Gender Critical” views do not meet that criteria, but we live under a judiciary that has ruled that they do and we have to deal with the consequences until that gets fixed.)
Opposing this is the fact that pubs aren't normal businesses. They're licensed premises and the powers and duties of a licensee are different.
All licencees, and their representatives (ie, anyone employed by the establishment) have a legal duty under the Licensing Act 2003 to prevent 'disorderly conduct' of any sort on their premises and can eject people from said premises or refuse service to prevent disorderly conduct. Licensees are not required to give a reason for this and it is a criminal offence to refuse to leave a licensed premises when ordered to do so. It's a different calculus compared to other sorts of venues.
Successful discrimination cases have been brought against pubs refusing entry, particularly several cases bought by Traveller groups, but in this case the refusal was to hold an event which could be argued to lead to possible disorder (counter-protest, etc.), not turning people away at the door. I know of plenty of cases personally of pubs and hotels refusing to hold certain sorts of events for all sorts of reasons.
They're trying to play the homophobia angle because they know that in this case it's by far their best shot. Licenses premises are not required by law to hold politically charged events; indeed, I am pretty sure that GC groups have been turned away from other venues before for conferences etc. and not managed to get anything to stick legally, not just licensed ones.
The fact that this is happening in a city noted for its progressiveness when compared to the... less educated... parts of Britain is surprising.
As I said, it'll be interesting to see how this plays out.