The CDC has issued guidance that the COVID-19 vaccines and routine vaccines can be administered without regard for each other’s schedules including at the same time. As I understand it, there are a few reasons why this wasn’t always the case (including wanting to isolate COVID-19 vaccine symptoms and side effects from others at the start of the rollout).
That's basically what the pharmacist said: it's probably not a hazard, more like your data point on side effects is not going to be useful because of the co-mingling. Good to know that they nailed it.
Source: https://www.cdc.gov/vaccines/covid-19/hcp/faq.html