In my experience, no. I’ve taken some CS courses at Mudd as a Pomona student myself and I have never found the need to ask others what schools they come from. It is assumed that everyone is equally interested and competent in the classroom: no one is wearing a tag that lists what school they are from or anything like that. There is a heavy culture of collaboration, and students work together to tackle challenging problems. I’ve made friends from all the five colleges and hold them to equal regard.
@ucbalumnus Scripps CS majors are considered native Harvey Mudd CS majors or native Pomona CS majors depending on the track they pick. The link above about off-campus students says it very explicitly: “A student who chooses to major in CS at HMC will be considered identical to a HMC CS major with respect to advising and access to HMC CS courses.” Then it goes to explain that HMC CS majors have priority for some of the classes, which includes the off-campus majors who are doing CS.
I know it seems strange given the different admissions requirements for each school, but the Claremont Colleges heavy collaborate with each other and fill in gaps that the others may have. It’s one of the great highlights of the system that few other schools offer. Also, all of Harvey Mudd’s employment fairs and career information panels are open to students from all of the 5 colleges.