Yes, you can. But you should not have sex the first day after you insert a NeuEve suppository. This is written on the NeuEve box. You need to allow at least 1 day for the the suppository to be melt and dissolved so that it can have an effect.
Semen can dilute and neutralize the suppository ingredients. Wearing a condom may be best but latex condoms are not compatible with NeuEve as it is oil based. You may try polyurethane condom if you choose to use one.
You can have sex without a condom on the last day the suppository, before you insert a new suppository. Say you are using BV Clear suppository once every 3 days, the 3rd day after you insert a suppository is the last day. If you count the first day when you insert a suppository as day 1, the 3rd day after that is day 4.
If you are on a one suppository per week schedule, like BV maintenance or on NeuEve Gold, you can have sex on the 7th day before you insert a new suppository. However, if you cannot wait for 7 days, say you have sex on any day between day 2 and day 6, this may render the previously inserted suppository less effective, but it may not matter too much as the suppository is strong enough to overcome the semen effect. The ideal timing is on the last day of the suppository because you can allow it to work for a whole week. Nothing is wasted.
After sex, you must pee to avoid possible urinary tract infection (UTI) even if your partner uses a polyurethane condom. Urination can flush out bacteria that entered the bladder during sex. Therefore, drinking some water before sex can help build up the urinating pressure. It can produce a strong "power wash" to flush out bacteria in the bladder to prevent UTI.
If you are on BV maintenance and you have sex before the last day of the suppository and you smell odor after sex, you should insert a new BV clear or NeuEve Gold suppository after urination to prevent BV coming back.