In the West Wing was Evelyn Baker Lang based on Ruth Bader Ginsburg
and Christopher Mulready based on Antonin Scalia?
Short answer: Yes, but only partially.
Certainly, those characters are a reference to those two justices, RBG much more than Scalia, and there are significant differences as well.
I googled the writer of the episode, Deborah Cahn, and this was one of her first writing jobs for TV, but far from the last. She's had a very successful career, but as far as I can tell, she's never discussed this episode. Likewise, Glenn Close has never discussed the character that I can tell, so all we have to go on is the episode itself. If there is information by the writer or actor, I couldn't find it.
But, I did find an article by Clay Dockery, who had this to say:
That name is Christopher Mulready, who is played to mantis-like
perfection by William Fichtner. He is basically untenable to everyone
as a fiery conservative who has literally written books demonizing the
left. It is hard to say exactly who I think Mulready would be
analogous to in real life. While Lang and Mulready are obviously based
on Ginsburg and Scalia, Mulready is more than that. He is somehow a
combination of Scalia, Bill O’Reilly, and William F. Buckley.
I'll add a note that William Fichtner, who doesn't wear glasses, does wear glasses for this role making him a little bit more Scalia like in look.
Dockery goes on to say:
we can remember this: the friendship between Lang and Mulready was
based on real life friendship: the one between the departed sarcastic
and dominating Antonin Scalia and the dearly departed Notorious RBG
So, at least one writer's opinion is that there is a considerable amount of those two characters based on real life RBG and Antonin Scalia. Add to that, the undeniable similarity between the names "Evilyn Baker" and "Ruth Bader" - both women, both using 3 names, very similar middle name and the close friendship with an intelligent conservative. The comparison is clear cut and obvious.
But there are differences, and the differences are important and I'm going to pull a quote from the show to make this point:
TOBY I hate him. I hate him, but he's brilliant and the 2 of the them
together fighting like cats and dogs. But it works.
[Back in the Mural room]
SENATOR PIERCE You couldn't find a single warm blooded centrist to put
on the court?
JOSH We've got centrists. We've got 6 of them plus 2 staunch
conservatives plus Justice Ashland. The one clarion voice
articulating a liberal vision. He's going to go and then what?
Toby's line "I hate him. I hate him, but he's brilliant", feels like it could be a reference to Scalia. It's not much to go on, but it's the kind of thing a liberal like Toby might say about a justice like Scalia.
And the line "They'll fight light cats and dogs", where it was later revealed that they were or could talk like friends, also, could be a reference to Ginsberg and Scalia.
OK, now the differences:
In the show, a justice is talked into resigning so they can nominate a liberal and a conservative together and get them both through. That's not at all like RBG and Justice Scalia's nominations. Justices do resign, when there's a president they like and they want that president to replace them with a like minded younger justice. That happens, but never has a justice been asked to resign so a liberal and a conservative could be nominated together. That was 100% fiction.
Scalia was nominated in 1986, by Reagan and confirmed 98-0. Those were different times, but he was well spoken, intelligent, had a good record and democrats voted for him. He was also replacing a conservative and the parties were more civilized back then and the democrats had, I believe a 5-4 lead in the court, so nominating a conservative didn't raise any red flags.
Ruth Bader Ginsburg was confirmed in 1993, 96-3 after a somewhat more contentious congressional confirmation where she refused to answer some questions, but she was still widely regarded as capable and qualified, by both parties and like Scalia, she didn't tip the balance of the supreme court. We might never see a 96-3 vote again. Those were different times.
The nomination process in the show had absolutely NOTHING in common and with those two justices.
And while I think Senator Pierce's line is funny "You couldn't find a single warm blooded centrist to put on the court?" - cause, that would make sense, right? Nominate someone the two parties could get behind, not one far left and one far right, Josh's line that follows, takes us far away from our world and deep into a fictional world:
Josh: "We've got centrists. We've got 6 of them plus 2 staunch conservatives plus Justice Ashland". Ashland, in the show, had health issues, and he stepped down so Lang could be nominated, but he also stepped down so they could get Lang and Mulready in together . . . it was a convoluted and completely fictional set of events.
And this breaks cannon, because it ignores Justice Mendoza and the whole point behind him was that he was a liberal and Bartlett wanted to nominate a centrist who would get in.
and . . . I might add, RBG never had an abortion like Evelyn Baker Lang. The differences are sufficient, that to me, the 2 characters are a reference to, and in parts based on, but not really based on either real-life justice. The differences are too many.
Now, some of the characters in the show are loosely based on, or inspired by real people, but even then, the comparisons only go so far.
CJ Cregg was based on, or perhaps more accurately, inspired by Dee Dee Myers, who consulted with Aaron Sorkin on the show quite a bit.
Josh Lyman is loosely based on, or takes some inspiration from Rahm Emanuel
Sam Seaborn is believed to be based on or inspired by George Stephanopoulos
Matthew Santos (played by Jimmy Smitts) is obviously, but I think, quite loosely, based on at the time, Senator Obama and President Bartlett is, often said to be based on Bill Clinton, who Martin Sheen met after he started filming the show and liked quite a bit. There are references that President Bartlett also draws inspiration from JFK and Jimmy Carter, but I think the strongest character influence came from Aaron Sorkin's father, who Sorkin describes as a man who loved books and literature and antiques.
The show hasn't been shy about identifying that "this character is based on or inspired by that person", but it's rarely to never a full imitation. It's a few things in common, a shared story or shared experience, which might be more accurately termed as "inspired by" not based on.
Finally, I want to say a word or two about this episode. In some ways it's brilliant. It has snappy dialogue. It covers a lot of ground in the 42 minutes or whatever it is, and Glenn Close plays a memorable and fan favorite character with barely 5 minutes of screen time. The fact that she's a "liberal longshot" who they didn't think could get in, then they met with her, fall in love with her and have to figure out a way to get her nominated, rather than just a woman on the short list, is clever, it's a lot of moving parts and it allows the actors, especially Glenn Close, to shine.
The whole "she's too liberal" is very 2000s and not at all like RBG who stood her ground, refused to answer some questions and still got 96 votes. So, the show also borrows from party partisanship that had begun to surface after RBG's confirmation.
And while the show has a centrist theme, William Fichtner plays Mulready like a snake, compared to the heart and intelligence that Close shines with, I think that undermines the centrism outline of the episode. The final product is liberals shine and conservatives have snake venom in their blood. . . . and as a liberal myself, I can watch that and not mind it, but in no way is that a reference or fair tribute to Scalia, who I mostly disagree with, but at least he was well spoken. This episode casts Mulready as much more of a talking point conservative.
I came to your question while researching a comparable West Wing question of my own on whether Daniel Gault was based on the Rosenbergs . . . which I haven't posted yet, but your question interested me and I did some research on it as well and I came to the same conclusion for your question as I did to my own (which I haven't posted . . . I still might).
The show borrows from real characters and events, but it mixes in a good deal of fiction. It's television after-all and they crank out an episode every week. It's done on a tight schedule.
Glenn Close nailed the role, and while some of the references are obvious, a lot of this episode is pure fiction. I love the West Wing, but I think most of the real life comparisons are superficial.
So, I'd call it a reference to, but I wouldn't say it's "based on", though it's based on elements of RBG's life and her relationship with Scalia. I don't think it's based on Scalia much at all, outside of maybe a line here or there and a pair of glasses.