Mentioning MBA part-time hurting my chances of getting hired?

Some thoughts and just my $0.02. Having work experience is a critical part to gaining value from an MBA (regardless of whether it is part time or full time). This is why almost all programs require at least 2-3 years of full time work experience before applying--people simply have personal experiences to share with the classroom and the overall experience is more valuable with these perspectives added.

Another point--compensation post-MBA largely is based on the fact that candidates have experiences under their belt AND an MBA. The bump most people receive is commensurate on their skills they have developed pre-b school and the quality of the MBA (which is why the higher you go in rankings, the higher the salaries). Your odds of being compensated fairly (your definition of fairly is unique from anyone else's of course) are very limited in a part time program because the big bump in pay comes from leaving a job after getting the degree OR getting a new one after finishing a full time program. An employer may struggle figuring out how to price this in given they don't even know what your work product is before hiring you, not to mention what your hidden agenda might entail given your additional time and investment spent in school part time while working for them.

Networking and opportunities sourced through your school (on campus and the alumni network) are key to landing a job in real estate. I don't know if telling employers you are doing an MBA part time at age 22 (assuming you are this age coming out of undergrad) is wise as many candidates bounce after getting the degree in search of a pay raise or better opportunity elsewhere. They may see this as a risk in hiring someone who is already pursuing the MBA without work experience. Others may disagree but this would be my thought process. I frankly don't know if there is any value in sharing with employers that you are starting a part time MBA. They will want you 100% focused on your role with them and any part time schooling is obviously a detractor from that notion.

Lastly, b-school is a unique time that should not be taken lightly. It is one time when you can hit the reset button, and even change careers. This is another reason why people typically wait a couple years to go back. If you find out that you really don't like real estate (which could happen, given that odds are against all of us in knowing 100% what we want in life at age 22), you would have an MBA as the opportunity to explore those options. So all in all, I wouldn't mention it to employers (until you land a job--then maybe mention it if need be), and if at all possible I would personally reconsider the MBA this early in your career for the reasons outlined above.