Given the size of the antennas it sounds like you dealing with frequencies in the microwave spectrum.
Assuming this to be the case then different types of tape would have an effect on the tuning of the antenna, I've used ptfe tape to re-tune PCB filters to a lower frequency just by sticking it to the substrate.
Useing the wrong tape could affect the VSWR at the required frequency of operation. If you have a VNA available to you, run a sweep on the antenna and observe s11 for your centre frequency for different types of tape.
Also... non ESD tape could generate a significant static charge that could kill or damage the input device of your receiver. Most microwave devices are very static sensitive and ESD rules apply when using them.
If you have an ESD meter, use it to measure the static potential as you remove the tape from the device.
Google "sticky tape static charge" for more info.
regards
Tim