How secure is it to recycle my old mac computer at an apple store

Remember you are asking other end users here, not Apple nor its recycling partners. We cannot know their procedures nor give you an official answer.

If you are worried, first review the FAQs that Apple have published here:

Apple Trade In

Otherwise, I concur with Jeff's excellent advice. No computer leaves my control with a hard drive having accessible data.

How old is it? There was a feature in /Applications/Utilities/Disc Utility.app to securely erase a conventional hard drive when initializing it. That is not an option for an SSD drive, however. You can enable FileVault so that the contents of your personal files on the hard drive are encrypted. You would want to use a complex admin user login password that can not be cracked, ie NOT "password" :-)

Protect data on your Mac with FileVault - Apple Support

also from the Finder Help Menu: macOS User Guide "If you have a Mac with Apple silicon or an Apple T2 Security Chip, your data is encrypted automatically. Turning on FileVault provides an extra layer of security by keeping someone from decrypting or getting access to your data without entering your login password. If you use a Mac that doesn’t have Apple silicon or the T2 chip, you need to turn on FileVault to encrypt your data."

System Settings

If you have concerns about data retrieval, rather than worry about that possibility after recycling the computers, I'd recommend taking a preemptive measure and remove the hard drives before dropping them off. With that done, you'll never have to give the matter a second thought. If you post back regarding the type of Apple computers that you have (mini-tower, laptop, tablet), the level of difficulty involved can be assessed and any technical guidance provided.