Do I need to worry about differences in produce in foreign recipes?

tl;dr: Yes, there are significant differences ... but use them as guidelines, don't just blindly follow recipes. (Jacques Pépin agrees)

Part of the size issue that Jefromi mentioned is not only growing conditions (hotter/dryer/morning sun/in a greenhouse/etc), but there are typically different varietals of things.

Eggplant is one of the most significant -- In the US, we have in some shops 'japanese' or 'chinese' eggplant, which is a long slender thing ... but the typical US eggplant is the 'globe eggplant', a bulbous dark purple variety. Indian eggplants tend to be smaller in size, firmer, more egg-shaped, and are much more difficult to find in the US unless you're growing your own.

For cucumbers, the ones we used to have in the shops were about 8 inches (20cm) long, thick skinned with rather significant seeds. These days, I mostly find the 'English' cucumbers that are longer (over 12"/30 cm), skinnier, with thin skin and smaller seeds. But some shops will also carry 'Persian' cucumbers, which are much smaller (under 6"/15cm). Where and when the recipe was written will greatly affect what is meant if they don't qualify the cucumber.

There's also significant variation in hot peppers. In your area, 'crushed red pepper' might be Allepo pepper, which is much fruitier than the variety used in the US. (I'm not even sure what variety it is -- it might be cayenne)

We also have things like 'oregano'. Mediteranian oregano (origanum vulgare) is a member of the mint family, while Mexican oregano (lippia graveolens) is in the verbena family.

Although flat leaf parsley is often the only 'parsley' in US shops these days, for years curly parsley was unqualified (just 'parsley'), while flat leaf was called 'chinese parsley'

Apples are another item with significant regional differences -- in part because they're typically bred for thrive in a specific growing condition, so many American varieties aren't available in Europe and visa-versa. When I lived in the Netherlands 30 years ago, the typical apples in the shops were tart green apples, similar to the Granny Smith in the US.

Carrots have also changed rather significantly in the US. 'Baby carrots' were originally a way to sell broken carrots that would otherwise go to animal fodder, but as they could sell for a higher price, many farmers started growing more slender varieties where the majority of the carrot could be turned into the pre-processed "baby carrots". In my area, the only places that I know to get decent sized carrots (as large as the old 'winter carrots') are in international grocery stores or Restaurant Depot (if I need 50lbs).

... I'm sure that I could go on, but unless you're baking, you can taste as you go and adjust however you like. If you've never tried the dish you're trying to make, it just looked interesting, you can always use it as guidelines ... if you think it looks dry as you had smaller tomatoes, go ahead and add some more. If you've had the dish before, you have more of a target of what you're aiming for ... but that still doesn't mean that you have to strictly stick to a recipe.

In general, things should be quite similar, and the biggest thing you'll have to worry about is size. There can be really drastic differences in the "normal" size of a given thing from country to country; a large onion in Egypt might be half the size of a large onion in the US.

So if you can find recipes that specify actual quantities, whether weight or volume, you'll be a lot safer than with recipes that just say "one large onion". European recipes are more likely to specify ingredients by weight than American ones, but that may not always extend to things like onions.

You'll also have an easier time with recipes that have some wiggle room. It doesn't matter that all that much if you have 30% more tomato in your salad than you meant to, but if you're making a sauce with the tomatoes providing a lot of liquid, the texture might end up off if the quantities are off.

Beyond that, I'm sure there are some specific ingredients where you'll run into local differences, e.g. maybe your "normal" onions are similar to US onions, maybe they're a little sharper, maybe they're a little sweeter. But it's going to be really hard to predict exactly which things will differ, and hard for anyone to answer unless they've lived both places.

All recipes require some amount of adaptation to your own conditions. Even if the author of the recipe lives next door to you and buys exactly the same ingredients as you, you'll need to make some adaptations because, e.g., your oven might be hotter than theirs, or your wider pan might cause things to evaporate more quickly and require more liquid to compensate. Cooking isn't a process of robotically following instructions.

So, yes, you'll probably need to adapt recipes slightly. Differences in produce may mean you need slightly different cooking times and slightly different quantities – for example, if your local onions are bigger than my local onions, you might only need half an onion when my recipe says to use a whole one. If you're baking, fairly exact quantities tend to be quite important but, for most other things it doesn't matter. If you use more onion than the recipe writer intended, your food will have a bit more onion flavour; if you use less, it'll have less onion flavour and the sauce might not thicken quite as much. Neither of these things is wrong or bad.

While there is certainly a difference in what is known as terrior (the environmental influences on the characteristics of a crop) for a variety of products, I doubt that this difference would impact your recipes. In other words, you would likely taste a difference if you were able to compare American garlic and Egyptian garlic side by side, but for most recipes you can replace with local ingredients without worry.