What type of profile will I get for Moderate Asthma? National Guard?

What you are wondering about are referred to as the "Standards of Medical Fitness". DoD publishes instructions in DoDI 6130.03 volumes 1* and 2*. Volume 1 covers that standards for "coming into the military" while Volume 2 addresses those for "staying in the military". The Army incorporates those into the Service regulation AR 40-501*.

To your specific question, "is it feasible to have restrictions place on running activities?". The answer is yes. The more pertinent question is how severe are those restrictions?

If it's just that you can't run, then you need to have a medical profiler issue you one (probably a U2) for running. You'll then take an alternate event during the ACFT. The alternate aerobic events for the ACFT are the 2.5 mile walk, 12 km bike, 5km row, or 1km swim*. If you can do that, then you'll hardly make anyone blink.

However, if you can't do an alternate aerobic event (you must be able to complete at least one aerobic event to complete the ACFT), then you'll likely be referred to a MAR2* either because you will be given a P3 or P4 profile (which triggers a MAR2) or because of a commander referral because you can't complete the ACFT.

In AR 40-501, section 3-13b covers asthma. You'll have to evaluate your condition against those standards. If you can't meet those standards, you'll be referred to a MAR2.
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* DoDI 6130.03, Vol 1 - https://www.esd.whs.mil/Portals/54/Documents/DD/issuances/dodi/613003_vol1.PDF
* DoDI 6130.03, Vol 2 - https://www.esd.whs.mil/Portals/54/Documents/DD/issuances/dodi/613003_vol02.PDF
* AR 40-501 - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN37720-AR_40-501-002-WEB-4.pdf
* ACFT events, including alternate events - https://www.army.mil/e2/downloads/rv7/acft/ACFT_scoring_scales_220323.pdf
* ACFT FQA - https://www.army.mil/acft/#faq
* MAR2 process - https://www.hrc.army.mil/content/5503

SPC (Join to see) While you wait for other responses, here is a previous post that might help. You can search on "Asthma" for other posts. Good luck.

COL Randall C.

https://www.rallypoint.com/answers/can-i-serve-my-time-in-the-army-if-i-am-diagnosed-with-asthma

I think it depends on how bad it is and what they diagnose. But yes you can get a profile for at your own pace/distance. I've had one because of my knees since 2016 and I'm active duty. I did the walk on the APFT. Now I do the row machine on the ACFT. And there's also bike, swim or 2.5 mile walk as options in lieu of the run.