I stopped putting a lot of plastic in the recycle bin. The main reason because it's not recyclable - you're just increasing the cost to recycle. It needs to be sorted out and as a result cost more... It feels bad but I think it is better... For example a cereal box - has the plastic inside and the paper outside... I take the plastic out into the trash and put the paper into the recycle...
Whoever is picking up your recycling will have info on what can and cannot be recycled. If you're concerned I'd reach out to them and they should be able to give you a list of recyclable items. For me they only accept plastics with a number in the symbol except numbers 3 and 6, no plastic bags, and items must be thoroughly cleaned.
It's also regional, so friends of mine a few cities away have a totally different list of what they can recycle because its based on the capabilities of the facility it ends up at.
It's much more confusing and stupid than that. You can't rely on the symbol and the number because the forming process used on items like bottles and clamshell packages affects whether they can be recycled or not (which in addition is a function of the local recycling processes, which vary). I found this out because our recycling center posted notices saying that only bottles with narrow necks can be recycled, and if they find more than a fraction of the "wrong" plastic in a batch, it all goes to the landfill.