Zoo memberships - like many non-profits - can be fully deductible, partially deductible, or not deductible at all, depending on their charter papers, the type of 501(c) organization that they are, and whether or not you receive tangible benefits for your membership (the value of these must be subtracted from your membership fee).
In the past, these memberships (or part of the fee) would have been deductible as a charitable contribution. The Tax Cut and Jobs Act of 2017 did not change this. Perhaps the person who told you this meant that because the Standard Deduction has doubled, that most taxpayer would not be able to use their itemized deductions.
We at the AnswerXchange have no way of knowing the details for the Philadelphia Zoo. I encourage you to contact the Zoo at 215-243-5254 (Member Services) and ask them to be sure.