Is it good practice to send operational emails from a different provider than promotional emails?

This is a very important consideration when formulating and optimizing an effective email communications system. And the answer is pretty straightforward.

First, let's clarify the two types of emails under discussion:
1. Transactional (or "operational") email: eg, registration confirmations, password reminders, friend/follower notifications, purchase receipts, and shipping notifications.

2. Marketing ( or "promotional," bulk) email: eg, newsletters to subscribers & customers that typically highlight new product/service features, special offers, company news, etc.

The primary consideration here is that these two types of emails are received and treated differently by the end recipient...
Marketing emails are usually less critical in nature and thus more likely to be perceived (and even flagged/reported) as spam, even if the customer opted-in to receive them.
Transactional email is generally more critical in nature - ie, when a customer *doesn't* receive this type of message, they think/know something is wrong and probably contacts customer service to investigate.

So the answer to your question is YES - deliverability of promotional emails can very easily (and often times does) negatively affect deliverability of operational emails.

However, there is a more simple solution than using two different vendors...

The main goal to eliminate the effect of one on the other is to separate the traffic onto different IP addresses. With SendGrid, we can provide one IP address for transactional/operational emails and a separate IP address for marketing/promotional emails. This not only isolates the reputation and deliverability for each type, but it also aids in distinguishing the performance/statistic on each email category.

I hope this helps. I tried to be as thorough as possible, without going into too much detail. I'm happy to answer any follow-up questions!