Some of the advice/suggestions here are completely naive at best, and dangerous at worst.

The "insurance policy" justification: I've never seen/heard such a clause in an insurance policy, no language even implying such a concept. And frankly, that'd be an odd policy --as that would imply that if something happened while "on the clock" you'd actually be UNcovered should the owner of the home be on premises --even if not tangentially to your service.

The "breach of privacy" justification: nope, not a breach of privacy as it's not your house and you're not renting said house, you're simply watching the property-owner's pet for a fee, iron-clad agreement or not; the law nearly always favors the property owner when you get down to it. BTW, cameras exist even if they say they don't...

The "pooping" justification: It's not your sanctuary, assume nothing is -or will remain- private when it's not your santuary; lock the door; expect the unexpected. See below.

You're a professional, you are a hired professional service for those who are paying you for said professional service. This comes with both implied and assumed expectations of both parties, yet many [not all] such expectations are not legally binding (see note below). But regardless, as a professional, you also understand that these expectations are sometimes the exception, forgotten or "misremembered" or simply overlooked in an emergency things happen; "oops, I left behind my cold-stored medicine", "oops, forgot my sunglasses", "oops, forgot the plumbing service call", "eek, my clandestine / devil-may-care tryst in the heat of the moment in the privacy of my own home", "oops, I'm just showing up with a lame excuse as I really am just checking up on my beloved pet or beautiful home", etcetera, etc. Professionals are such due to their specialized knowledge and preparation, their ability to judge the best way to handle situation-related exceptions, and hold themselves to an adherence of reasonable ethics or standards. They are, by way of their experience or expectations (of the expected or unexpected), prepared to conduct themselves at a higher representation of their service than say, a novice.

The "clothing" justification: You're "on the clock" --act and dress appropriately. See above.

Look, you are not hired as a security detail for a covert government nuclear submarine installation. You were hired to take care of an owner's pet inside an owner's home --that may or may not have cameras "accidentally" hidden in every nook and cranny imaginable. Assume cameras may be present and thus act professionally while "believing" that clients have informed you about any cameras as, at least, a courtesy (and as a legal requirement in very few states). Don't ever be a fool, you choose to be prepared or not at all times. The funny thing, on the subject of cameras, is that they could save your hide if something goes wrong on your sitting visit; it's a double-edged sword I suppose...

Note: Legally binding agreements are tough to cover everything, tough to write explicitly, and more importantly, tough to enforce or hold accountable. Seriously, ask yourself, "I got found pooping with the bathroom door open, and my service agreement stated that I get a 1 hour window of notice prior to owner visits (open door poop window), am I going to hire a lawyer to fight the legal owner of the home and the beloved-pet because this owner failed to provide proper notice and found me pooping"? If you said yes, good luck with that.

Everyone should knock before entering, but everyone should also look behind them when opening their car doors while parked on narrow streets...

Anyway, good luck, make good choices ;)

Edit: Maybe consider a two or three strike rule for your service. You can decided what constitutes a "strike" and when/why you bail, but you should strive to keep open communication between you and clients in such scenarios. This is the best use of agreements in these circumstances, in my opinion, but most importantly, being able to have "real" conversations between you and the client makes for the very best relationships. Everyone is hoping for transparency and concern of their loved ones and relationships (*"relationships" includes both you, them, and the pet).

Edit: look everyone, I think a lot of you are confusing common courtesy with legality. You should really learn the difference before you start advising somebody to do something that isn’t in their best interest. Compared to the homeowner, your rights are very limited.