Let's imagine I'm answering this question as part of the 80% of people building websites with ExpressionEngine who may consider themselves as designers and or people who have little to no PHP experience:
Is it ever acceptable to use PHP inside ExpressionEngine templates?
No it's not acceptable, please don't do it!
Or is this considered bad practice?
Yup, pretty much.
If you were a developer who inherited a site I coded, would you cringe
if you saw PHP inside templates?
Definitely would cringe and maybe even curse a little.
Okay, now let's imagine I'm answering as part of the 20% who would consider themselves as an EE developer and or who have most experience programming over say designer all day:
Is it ever acceptable to use PHP inside ExpressionEngine templates?
Once in a while it's acceptable. For example you might find a need to turn on PHP for this Stash setup. It really depends on the complexity of what you are trying to achieve. Most things should go into an add-on whenever possible and being "lazy" doesn't count as a time when PHP is acceptable in templates.
Or is this considered bad practice?
ExpressionEngine and Codeigniter for that matter provide a great base to build add-ons and best practices include proper separation when ever possible. This includes separation from PHP and Templates; more often than not.
If it can go into an add-on it should as mentioned before. With that said, there isn't really anything limiting you from using PHP in templates except knowing that this may have security implications, cause future headaches for clients and other devs/designers etc.
If you were a developer who inherited a site I coded, would you cringe
if you saw PHP inside templates?
Definitely wouldn't cringed (unless your PHP was a disaster right from the start) though, would probably question why such simple and even complex code wasn't where it belonged; in an add-on.
Note: I pulled the percents out of thin air though, they quite possibly could be close to reality.
Also note: I realize the use of designer/developer in my answer could be seen as stereotyping though, wasn't quite sure how to avoid it. Hope no one takes offense.